Farrar was born in Halifax. Her mother was Louisa Frances (born Hincksman) and her father was Joseph Farrar and he made textile machines.[1] She was named after Dorothy Hincksman who had been a nineteenth century missionary.[2] She was educated at the private Methodist Oakfield School in Arnside. This was a boarding-school. She went on to Bedford College which following her graduation she later studied further and gained a doctorate in 1931 in psychology.[1]
Her mentor was Revd Dr Russell Maltby who was a keen supporter of women and Warden of the Wesley Deaconess Order.[3] He encouraged her to preach in Halifax where she had a mixed reception. Some were very supportive, but others would leave the service as she began to speak without listening any further.[1]
Farrar became a deaconess in 1936 and she started teaching at the Wesley Deaconess College where she had trained in Ilkley.[1] Her mentor Rev Maltby was still the warden until 1940.[3]
In 1952 she was the second woman ever elected to be vice-president of the annual Methodist Conference.[4] Farrar retired in 1962.[5]
In 1978 it was decided to stop recruiting any further Wesley deaconesses and this was a disappointment to her.[2] However, in 1986 the Methodist Diaconal Order which accepted both men and women was seen by her as a good replacement.[5]