It mirrors US relations.
The same as with the US, normal relations.
Australia had nothing to do with the Vietnam War.
They followed the US's lead. What the US did, Australia did.
Relationships between Australia and Vietnam are generally along the same lines as the relationship between the US and Vietnam.
Australia's relationship with it's allies (USA, SOUTH KOREA, AUSTRALIA AND NEW ZEALAND), US combat troops were involved from 1965 until their official withdrawal in 1973. Australian and New Zealand troops were involved from 1962 to 1973. the war ended on the 30th/APRIL/1975 and their relationship have stayed they same.
Australia never fought Vietnam.
Australian society mirrored American society after the war, on a smaller scale, due to population differences.
Part of SEATO (Southeast Asia Treaty Organization) & ANZUS (Australia New Zealand United States treaty).
Australia entered the Vietnam War because Australia feared that they would have to face the spread of Communism.
Yes, Australia fought in the Vietnam war on the side of the capitalists. They joined the war as a coalition with the US as a proxy war of the Cold War, and fought against the Vietcong and communists in an effort to prevent the Domino effect, an ideological security issue. Furthermore, Australia joined to retain the special Great and Powerful Friends relationship it has with the US in its usual sychophantic manner.
President Johnson's visit to Australia during the Vietnam War was met by Australian anti-war protests.