According to marriage records in Montpelier, there was a Sally Carter of Barnet married 04-06-1818 to Eliaser Picker. 
Who the father of Sarah\Mercy\Sally Carter was is currently a mystery. There are at least three Benjamin Carters who could be the father. Different sources point to one or the others as being her father. Until the birth record for Sarah\Mercy\Sally can be found with her parents' names, or, some other proof of her parents, then they will remain a question. 

Timeline (with accompanying Image ID's) for Sarah\Mercy and her parents: 
- 1747, Oct.11 in Sutton, Worcester co., MA birth of Benjamin Carter to Benjamin and Sarah [?Stone or ?Runnels] Carter, four older children also born in Sutton. These possibly are the ancestors. - I__0008,I__0200 
- 1777, Mar.13 in Sutton, Worcester co., MA marriage of Benjamin Carter Jr. to Mercy Gale. First two children born in Auburn, Worcester co., MA and the rest in Newfane, Windham co., VT. - I__0007,I__0014 
- 1795 in Newfane VT birth of Sally Mercy Carter per her ancestry.com family profile, she died 1866 in W.Brattleboro VT and was the wife of Eli Miller, they had eight children including John B. Miller. The record says she was the daughter of Benjamin Carter (1847-1826) and Mercy Gale (1750-____). - imageID:I__0198 
- 1813, Jul.18 in Brattleboro, marriage record of Eli Miller and Sally (or Mercy) Carter, they were married about the time "another Benjamin Carter" died (in 1814) - imageID:I__0202 
- 1850 census for Brattleboro, VT includes Eli Miller age 60 b.VT and wife Sally age 55 b.VT and daughter Sarah age 17 b.VT - imageID:M__0192 
- 1860 census in Brattleboro Sally (Carter) Miller on age 65 b.VT - imageID:I__0199 
- 1866, Nov.29 death record in Brattleboro VT of resident Sally Miller, daughter of Benjamin Carter and Patty _____ [?? vs. Mercy Gale or even Polly Burnett]  - imageID:I__0196 
- 1866, Nov.29 death in Brattleboro VT of Sally Miller, daughter of Benjamin Carter and Patty _____ [?? vs. Mercy Gale or even Polly Burnett]. This is a rare document with the names of her parents. - imageID:I__0197 
- 1883 death record for John B. Miller says his parents were Eli Miller and Sally Carter - imageID:I__0180 
- Gill, MA vital records typed family sheet says ancestor Sarah Carter (1795-1866) born in Newfane VT and was the daughter of Benjamin Carter (1747-1826 in Gill) and Mercy Gale. For Benjamin and Mercy, child #2 is Benjamin b.1785 in Auburn, m.1806 in Gill to Mary Burnett and had six children and child #7 is ancestor Sarah b.1795 in Newfane, married Eli Miller, she died 1866 in W.Brattleboro. - imageID:I__0195 

Carters in western Massachusetts and southern Vermont in the 18th and early 19th centuries: 
 - WORCESTER county MASSACHUSETTS <<>>: 
 - - Sutton: 1747, birth of Benjamin Carter Jr. to Benjamin Carter and Sarah ______ who had four children here prior to Benjamin Jr. 
 - - Sutton: 1777, marriage of Benjamin Carter Jr. and Mercy Gale 
 - - Auburn: first four (of seven) children born here (but ancestor Sarah\Sally\Mercy born in Newfane) 
 - WINDHAM county VERMONT <<>>: 
 - - Newfane, 1795 birth of Sally Carter to Benjamin Carter and Mercy Gale 
 - - Brattleboro: 1813 marriage Eli Miller and Sally Carter 
 - - Brattleboro: 1850, census with Sally (Carter) Miller, age 55 b.VT, and Eli Miller 
 - - Brattleboro: 1860, census with Sally (Carter) Miller, age 65 b.VT, and Eli Miller 
 - - Brattleboro: 1866, death of Sally (Carter) Miller 
 - - Brattleboro: 1866, burial of Sally Mercy (Carter) Miller 
 - FRANKLIN county MASSACHUSETTS <<>>: 
 - - Gill: 1806, marriage of Benjamin Carter and Polly Burnett, https://www.familysearch.org/tree/person/details/LK8S-53B 
 - - Warwick: Benjamin, birth, son of Benjamin and Polly Carter 
 - - Warwick: 1814, death of Benjamin Carter, husband of Polly 
 - CALEDONIA county VERMONT <<>>: 
 - - Wheelock: 1814, death and burial of Benjamin Carter (1764-1814), a private in Revolutionary War, buried with wife Elizabeth (Blaisdell) Carter, https://www.findagrave.com/memorial/33925097/benjamin-carter 

From a book about Rev. Thomas Carter: 
 - - Benjamin, child #4 of Thomas Carter and Abigail Locke, b.1722, baptised soon afterwards in Weston MA 
 - - Benjamin, son of Thomas Carter, mentioned as deceased in the 1768 will of Thomas in Litchfield CT 
 - - Benjamin, son of Thomas Carter, d.1774 
 - - Benjamin, Lt. who was of Hebron 
 - - Benjamin, child #5 of widow Anna Carter and Thomas Carter Jr., b.1755 d.1774 
 - - Benjamin, Lt., son of Thomas, b.1722 Weston MA, d.1760 Hebron MA, m.1760 Hebron to Phoebe Sawyer 
 - - Benjamin, son of Lt. Benjamin, b.1762 (and maybe died 1774 or 1853)

Historical
1795: France - The Marseillaise officially adopted as the French national anthem
1795: Georgia - Mohammad Khan Qajar razes Tbilisi to the ground
1795: United States, Spain - The Pinckney Treaty between the United States and Spain granted the Mississippi Territory to the U.S.
1795: United States - Kamehameha I of the Island of Hawaii defeats the Oahuans at the Battle of Nu uanu
1796-1804: China - The White Lotus Rebellion against the Manchu Dynasty in China
1796: Africa (western) - Mungo Park, backed by the African Association, is the first European to set eyes on the Niger River in Africa
1796: Ceylon, England, Naterlands - British ejected Dutch from Ceylon
1796: England - Edward Jenner administers the first smallpox vaccination, smallpox killed an estimated 400,000 Europeans each year during the 18th century (including five reigning monarchs)
1796: France - Battle of Montenotte, engagement in the War of the First Coalition, first victory of Napoleon Bonaparte as an army commander
1797: France - Napoleon Invades and partitions the Republic of Venice ending over a thousand years of Independence for the Serene Republic
1797: United States - John Adams is elected to succeed George Washington as President of the United States, he serves one four-year term and his son, John Quincy Adams, will serve one term as President 24 years later
1798-1800: United States, France - Quasi-War between the United States and France
1798: Ireland - The Irish Rebellion failed to overthrow British rule in Ireland
1799: France - Napoleon staged a coup d etat and became dictator of France
1799: India - Dutch East India Company is dissolved
1799: Tonga - The assassination of the 14th Tu I Kanokupolu, Tuku aho, plunges Tonga into half a century of civil war
1800: England - The Company of Surgeons are awarded their Royal Charter and became the Royal College of Surgeons of England
1800: United States - The Inception of the Second Great Awakening for the United States
1801-1815: United States, Africa north coastal countries - Barbary War between the United States and the Barbary States of North Africa
1801: England, Ireland - The Kingdom of Great Britain and the Kingdom of Ireland merge to form the United Kingdom
1801: Pakistan - Ranjit Singh crowned as King of Punjab (made up of parts of India, Pakistan and Afghanistan)
1801: United States - Thomas Jefferson elected President of the United States by the United States House of Representatives, following a tie in the Electoral College
1803: Saudi Arabia - The Wahhabis of the First Saudi State capture Mecca and Medina
1803: United States, France - The United States buys out territorial claims of France in North America via the Louisiana Purchase, this begins the U.S. westward expansion to the Pacific referred to as Its Manifest Destiny which Involves annexing and conquering land from Mexico, Britain, and Native Americans
1804-1810: Nigeria - Fulani Jihad in Nigeria
1804-1815: Serbia, Turkey - Serbian revolution erupts against the Ottoman rule, Suzerainty of Serbia recognized in 1817
1804: Auastria - Austrian Empire founded by Francis I
1804: France - Napoleon crowns himself emperor of France
1804: Haiti, France - Haiti gains Independence from France and becomes the first black republic
1805-1848: Egypt - Muhammad Ali modernizes Egypt
1805: England, France, Spain - The Battle of Trafalgar eliminates the French and Spanish naval fleets and allows for British dominance of the seas, a major factor for the success of the British Empire later in the century
1806-1812: Russia, Turkey - Russo-Turkish War (eighth of ten), Russian victory
1806: Europe - Treaty of Pressburg (Bratislava, Slovakia), Holy Roman Empire is dissolved as Francis II renounces his title as Holy Roman Emperor and becomes Emperor Francis I of Austria
1807: England - Britain declares the Slave Trade Illegal
1808-1809: Russia, Finland, Sweden - Russia conquers Finland from Sweden in the Finnish War
1808-1814: Spain - Spanish guerrillas fight in the Peninsular War
1809: France - Napoleon strips the Teutonic Knights of their last holdings in Bad Mergentheim
1810: Germany - The University of Berlin is founded, among Its students and faculty are Hegel, Marx, and Bismarck, the German university reform proves to be so successful that Its model is copied around the world (see History of European research universities)
1810: Mexico - The Grito de Dolores begins the Mexican War of Independence
1810s-20s: Latin America, Spain, Portugal - Most of the Latin American colonies free themselves from the Spanish and Portuguese Empires after the Latin American wars of Independence
1812-1815: United States, England - War of 1812 between the United States and the United Kingdom
1812: France, Russia - The French Invasion of Russia is a turning point in the Napoleonic Wars
1813-1907: England, Russia, Asia - The contest between the British Empire and Imperial Russia for control of Central Asia is referred to as the Great Game
1814-16: England, Nepal - Anglo-Nepalese War between Nepal (Gurkha Empire) and British Empire
1815: Austria - The Congress of Vienna redraws the European map, the Concert of Europe attempts to preserve this settlement, but It fails to stem the tide of liberalism and nationalism that sweeps over the continent
1815: Europe - combined armies commanded by the Duke of Wellington defeat Napoleon at Waterloo (Belgium), bringing a conclusion to the Napoleonic Wars and marks the beginning of a Pax Britannica which lasts until 1870
1816-1828: South Africa - Zulu kingdom of Shaka on the southeast coast of Africa becomes the largest kingdom in southern Africa
1816: northern hemisphere - Unusually cold conditions wreak havoc throughout the Northern Hemisphere, likely caused by the 1815 eruption of Mount Tambora on Indonesia, It is the largest volcanic eruption in recorded history and the most deadly as over 70,000 people died, the volcano ash caused what is called "volcanic winter" and 1816 became known as the "Year Without a Summer" because of the effect on North American and European weather where agricultural crops failed and livestock died resulting in the worst famine of th
1817: Serbia, Turkey - Principality of Serbia becomes suzerain from the Ottoman Empire, officially Independent in 1867
1819: France - Theodore Gericault paints his masterpiece The Raft of the Medusa, and exhibits It in the French Salon of 1819 at the Louvre
1819: Singapore, England - The modern city of Singapore is established by the British East India Company
1820: Liberia - Liberia founded by the American Colonization Society for freed American slaves
1820: United States - Missouri Compromise admits Missouri as a slave state and Maine as a free state
1821-1830: Greece, Turkey - Greece becomes the first country to break away from the Ottoman Empire after the Greek War of Independence
1821: Mexico, Spain - Mexico gains Independence from Spain with the Treaty of Cordoba
1821: Peru, Spain - Peru declares Its Independence from Spain
1822-1823: Mexico - First Mexican Empire, as the first post-independent Mexican government, ruled by Emperor Agustin I of Mexico
1822: Brazil, Portugal - Prince Pedro of Portugal proclaimed the Brazilian Independence on September 7, on December 1, he was crowned as Emperor Dom Pedro I of Brazil
1823-1887: England, Burma - The British Empire annexed Burma (now also called Myanmar) after three Anglo-Burmese Wars
1825-1828: Argentina, Brazil, Uruguay - The Argentina-Brazil War results in the Independence of Uruguay
1825: United States - Erie Canal opened connecting the Great Lakes to the Atlantic Ocean
1826-1828: Russia, Iran - After the final Russo-Persian War, the Persian Empire took back territory lost to Russia from the previous war
1827: England - Death of William Blake, an English poet, painter, and printmaker who Influenced literature
1828-1829: Russia, Turkey - Russo-Turkish War (ninth of ten), Russian victory
1830: Belgium, Netherlands - The Belgian Revolution in the United Kingdom of the Netherlands led to the creation of Belgium
1830: Colombia, Venezuela, Ecuador - Greater Colombia dissolved and the nations of Colombia (including modern-day Panama), Ecuador, and Venezuela took Its place
1830: France - July Revolution in France
1830: Poland, Russia - November Uprising in Poland against Russia
1830: United States - The Church of Jesus Christ of Latter Day Saints is established on April 6, 1830
1831-33: Egypt - Egyptian-Ottoman War
1831: France, Algeria - France Invades and occupies Algeria
1833-1876: Spain - Carlist Wars in Spain
1833: England - Slavery Abolition Act bans slavery throughout the British Empire
1834-1859: Russia - Rebellion led by Imam Shamil in Russian-occupied Caucasus
1834: Germany - The German Customs Union is formed
1834: Spain - Spanish Inquisition officially ends
1835-1836: United States, Mexico - The Texas Revolution in Mexico resulted in the short-lived Republic of Texas
1836: United States, Mexico - The Battle of the Alamo
1837-1838: Canada - Rebellions of 1837 in Canada
1837-1901: England - Reign of Queen Victoria is considered the apex of the British Empire and is referred to as the Victorian era
1838-1840: Central America - Civil war in the Federal Republic of Central America led to the foundings of Guatemala, El Salvador, Honduras, Nicaragua, and Costa Rica
1839-1851: Uruguay - Uruguayan Civil War
1839-1860: France, England, United States, Russia, China - After two Opium Wars, France, the United Kingdom, the United States and Russia gained many concessions from China resulting in the decline of the Qing Dynasty
1840: New Zealand, England - New Zealand is founded, as the Treaty of Waitangi is signed by the Ma-ori and British
1844: Haiti - Dominican War of Independence from Haiti
1844: Iran - Persian Prophet the Bab announces his revelation on May 23, founding Babism, he announced to the world of the coming of "He whom God shall make manifest", he is considered the forerunner of Baha u llah, the founder of the Baha I Faith
1844: United States - First publicly funded telegraph line in the world, It is between Baltimore and Washington and sends demonstration message on May 24, ushering in the age of the telegraph, this message read "What hath God wrought?" (Bible, Numbers 23:23)
1844: United States - Millerite (followers of the teachings of William Miller) movement awaits the Second Advent of Jesus Christ on October 22, the non-appearance of Christ becomes known as the Great Disappointment
1845-1846: Pakistan - First Anglo-Sikh War in Punjab (Pakistan) between the Sikh Empire and the British East India Company
1845-1849: Ireland - The Irish Potato Famine led to the Irish diaspora
1845-1872: New Zealand - The New Zealand Land Wars
1845: Tonga - Unification of the Kingdom of Tonga under Ta-ufa?a-hau (King George Tupou I)
1846-1847: United States - Mormon migration to Utah
1846-1848: United States, Mexico - The Mexican-American War leads to cession by Mexico of much of the modern-day Southwestern United States
1847-1901: Mexico - The Caste War of Yucatan
1848-1849: Pakistan - Second Anglo-Sikh War in Punjab (Pakistan) between the Sikh Empire and the British East India Company, this war basically ends the Sikh Empire
1848-1858: United States - California Gold Rush
1848: Europe - Revolutions of 1848 in Europe as some type of revolution occurred in most all European countries (except England and the Netherlands), the revolutions were quickly put down as they were mostly unorganized peasants
1848: Russia - The Communist Manifesto published
1848: United States - Seneca Falls Convention is the first rights for women convention in the United States and leads to the battle for suffrage and legal rights for women
1850: Europe - The Little Ice Age ends around this time
1851-1852: South America - The Platine War (also known as the War against Oribe and Rosas) fought between the Argentine Confederation and an alliance consisting of the Empire of Brazil, Uruguay and the Argentine provinces of Entre Rios and Corrientes, the war was part of a long-running contest between Argentina and Brazil for Influence over Uruguay and Paraguay, and hegemony over the regions bordering the Rio de la Plata (River Plate), the conflict took place in Uruguay, on the Rio de la Plata and in the northeast of Argen
1851-1864: China - The Taiping Rebellion in China is the bloodiest conflict of the century
1851-60s: Australia - Victorian gold rush in Australia
1851: England - The Great Exhibition in London was the first International Expo or Worlds Fair
1853-1856: Ukraine, France, England, Turkey, Russia - Crimean War between France, the United Kingdom, the Ottoman Empire and Russia
1854: Japan - The Convention of Kanagawa formally ends policy of Isolation by Japan
1855: England - Henry Bessemer Invents a process that enables steel to be mass produced from molten pig Iron
1856: Romania - First oil refinery in Romania
1857-1858: India - Indian Rebellion of 1857 (also known as First War of Independence for India, the Great Rebellion, the Indian Mutiny, the Revolt of 1857, the Uprising of 1857, the Sepoy Rebellion and the Sepoy Mutiny), It began as a mutiny of native soldiers (sepoys) employed by the British East India Company's army
1859: England - Charles Darwin publishes "The Origin of Species", It is a work of scientific literature considered to be the foundation of evolutionary biology, Its full title is "On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life", It presents a body of evidence that the diversity of life arose by common descent through a branching pattern of evolution and Includes evidence Darwin gathered on the Beagle expedition in the 1830s and his subsequent findings
1861-1865: United States - American Civil War between the Union and seceding Confederacy
1861-1867: France, Mexico - French Intervention in Mexico and the creation of the Second Mexican Empire, ruled by Maximilian I of Mexico and his consort Carlota of Mexico
1861: Russia - Russia abolishes serfdom
1862-1877: China - Muslim Rebellion in northwest China
1863-1865: Poland, Russia - Polish uprising against the Russian Empire
1863: Iraq - Baha u llah declares His station as "He whom God shall make manifest", this date is celebrated in the Baha I Faith as The Festival of Ridvan
1863: Switzerland - Formation of the International Red Cross is followed by the adoption of the First Geneva Convention in 1864
1864-1866: Peru, Chile, Spain - The Chincha Islands War was an attempt by Spain to regain Its South American colonies in Peru and Cile
1864-1870: Paraguay - The War of the Triple Alliance ends Paraguayan ambitions for expansion and destroys much of the Paraguayan population
1865-1877: United States - Reconstruction in the United States, slavery is banned in the United States by the Thirteenth Amendment to the United States Constitution
1865: United States - April 14, 1865, United States President Abraham Lincoln is assassinated while attending a performance at Fords Theater, Washington, D.C., he dies approximately nine hours after being shot on April 15, 1865
1865: United States - April 9, 1865 Robert E. Lee surrenders the Army of Northern Virginia (26,765 troops) to Ulysses S. Grant at Appomattox Courthouse, Virginia, effectively ending the American Civil War
1866-1868: Finland - Famine in Finland
1866-1869: Japan - After the Meiji Restoration, Japan embarks on a program of rapid modernization
1866: England, United States - Successful transatlantic telegraph cable follows an earlier attempt in 1858 by Cyrus West Field, the first cable used for telegraph communications laid across the floor of the Atlantic Ocean crosees from the Telegraph Field, Foilhommerum Bay, Valentia Island, in western Ireland to Hearts Content in eastern Newfoundland, messages that took at least ten days to deliver by ship now took only minutes
1866: Germany, Austria - Austro-Prussian War results in the dissolution of the German Confederation and the creation of the North German Confederation and the Austrian-Hungarian Dual Monarchy