Dunstan was born in Fiji to a rich Australian couple. He moved to Adelaide when he was a teenager, to go to school on a scholarship. He later studied law and arts at the University of Adelaide. He entered politics in 1953, getting a seat in the South Australian parliament at the age of 26. He became well known for his campaign against the death penalty during the 1950s, and his status in the Labor Party rose quickly. As a member of the opposition, he was able to get the parliament to pass changes to Aboriginal civil rights. He was also an important figure in his party's abandoning the White Australia Policy.