Australia joined the Vietnam war for many reasons. The major reason was Robert Menzies, the Prime Minister at the time, fear of communism and that the "domino theory" would come into effect (communism would keep heading south towards Australia) He tried to combat this through containment and forward defense. Another reason Australia joined the Vietnam war was Australia also joined the Vietnam to honour its treaties and show its support to the US as the US had helped Australia in WWII.
After the Cold War, Menzies was very afraid of communism. He was afraid that the domino theory would come into effect and Australia would be invaded by communism. To combat this fear of communism he sent 30 Australians in the role of "advisors" in 1962. This was part of his strategy of "forward defense" where the best form of defending Australia from communism was stopping the communists in South Vietnam (which was battling against its communist North Vietnamese neighbours).
This also meant that communism was stopped in Vietnam and would stop moving south, making Australia safe. Robert Menzies told Australians that if South Vietnam was taken over it would be a direct military threat to Australia and that South Vietnam had asked for Australia's help. But South Vietnam did not ask for Australia's help until after the government requested South Vietnam to ask Australia for help.
Another reason Australia joined the Vietnam war was to honour its treaties, particularly SEATO and ANZUS. SEATO's terms were that Australia would come to the aid of South Vietnam if under attack. ANZUS was a similar agreement which stated that Australia would come to the US's aid if they were attacked. The US played a very important role in why Australia joined the Vietnam War. During this time Australia was also fearful...