Farrar was born as Dorris Gertrude Wood in Bar Harbor, Hancock County, Maine, USA, on 6 June 1906. Her parents were George Fernando Wood (1878–1945) and Harriett M. Hadley (1881–1956). She had two sisters, Arleen Snow and Grace Kirsten. When she was around 8 years old, her family moved to New Britain, Connecticut, where she attended school.

In 1927, she graduated from New Britain General Hospital. In 1928, she married Earle Linwood Sawyer (1905–1969), with whom she had two daughters. The couple divorced at some point, and she remarried Raymond Munroe Farrar (1908–1981). She spent her nursing career both in Connecticut and in Massachusetts, until retiring at the age of 70.

In 2003, she returned to Maine. She stopped driving after turning 100. In December 2017, she was visited by U.S. Senator, Angus King, who presented her a certificate (on which her name was misspelled, something she herself noticed during the visit) and an American flag.

Farrar passed away in Freeport, Maine, USA, on 7 May 2018, at the age of 111 years, 335 days. She was survived by 2 daughters, 14 grandchildren, 40 great-grandchildren, and 17 great-great grandchildren.