Downer is part of one of the most remarkable political families in the state, his father was Sir Alick Downer, he was the High Commissioner to the United Kingdom (1964-1972). Sir John Dower, his Grandfather, was Senator in the first Federal Parliament (1901) and Premier of South Australia. Mary Lady Downer his mother was a descendent from the early immigrants of South Australia. He is also related to Sir Edmund Gosse an acclaimed English literary critic.
One of his early roles was as an Economist for Westpac Bank, then he became a Diplomat for the Australian Missions (European Union), after this he was ready to be an Embassy Representative (Belgium, Luxemburg) and finally becoming Minister for Foreign Affairs.
He attended school at Geelong in Australia before moving to the United Kingdom. He was enrolled at Radley College (1964-1970) and short after he was a student at The University of Newcastle (UK).
In 1975 he worked for the Bank of New South Wales as an Economist until 1976 when he entered the Australian Diplomatic Service, his service there lasted for six years (1982). Part of this service was held in Brussels where Alexander took a training course for French language. After serving he became an adviser to Malcolm Fraser the Prime Minister of the Liberal Party and Andrew Peacock successive Leader of the Federal Opposition. He also served for two years at the Australian Chamber of Commerce as an Executive Director (1983-1984), after this he was chosen as a Liberal member to the Federal Parliament in South Australia.
In 2014 he was assigned to be NATO’s Special Adviser to the Secretary General on Cyprus. Currently he works for the University of Adelaide.