Joan Marjorie Rochester was born in Victoria in 1931. She married Cedric Coxsedge in 1953 and had two sons and a daughter.
She became a professional artist in the 1960s and held four exhibitions of pen and wash drawings of historic buildings as well as undertaking a commission for the Builders' Labourers' Federation drawing Green Bans buildings around Australia in 1975.
As well as being an accomplished artist, Joan was a committed activist and politician. As a member of the Save Our Sons Movement which opposed conscription for the Vietnam War, she went to jail in 1971 for anti-conscription activities. She campaigned against the Croatian terrorist movement Ustashi in the early 1970s, opposed secret service organisations and was founding Chairman of the Committee for the Abolition of Political Police in 1973.
A member of the Australian Labor Party from 1967, Coxsedge contested unsuccessfully the Legislative Assembly seat of Balwyn in 1973 and stood for pre-selection in Richmond in 1976 against the Leader of the Opposition, Clyde Holding. She eventually became the first Labor woman to be elected to the Victorian Legislative Council as the Member for Melbourne West Province in July 1979 and served until 1992. While in office she wrote and produced the newsletter Hard Facts for Hard Times from her Footscray office, in which she offered a left view of current local, national and international events.
Coxsedge was involved with a large number of community groups and projects. She served as a Board Member of the Footscray Community Arts Centre (1980-98) and Chair of Board (1990-93); Board Member of West Theatre (1989-90) and Chair of End Child Prostitution in Asian Tourism (1993-98).