The Sixties in Australia were really the seventies. As for the actual sixties, in Australia, a couple of important things happened:
1966: The pounds-shilling-pence (Imperial) system was replaced by dollars and cents; and
1967: Aboriginal Australians were given the vote for the first time; Prime Minister Harold Holt disappears after going swimming, spawning a colloquial phrase "To do a Harold Holt" (both rhyming slang for "to do the bolt" and an evocative reminder of his departure) and the Harold Holt memorial swimming pool in Sydney, an ironic and gruesome namimg.
Of course, several other things happened, not least the conscription of many young boys who had been born in the post-WWII years into another pointless war, but these two points, at least, symbolised the drawing away from 'Mother England' and the White Australia Policy that had governed us culturally for so long.