Reasons for Australia's involvement in the Vietnam War were Australia's alliance commitments such as ANZUS and SEATO, the belief in the principle of forward defence, the fear of communism broken down into the areas of Menzies idea of "kicking the communism can" and his policy on anti-communism, belief in the domino theory and Harold Holt's "all the way with LBJ
and support for USA policy of containment.
Groups that supported the war were the Australian Liberal Country Party (something along those lines) and the RSL.
Reasons against Australia's involvement are it wasn't our war to begin with, Australia only joined the war to prove it's self as a valuable alliance to the United States, conscription or national service (unless under the grounds of moral objector) and the war lost support from the Australian people. It was a fail campaign to start off with, Douglas McArthur (commander of the UN) believed persisting with the war will not stop the threat of communism nor could Australia fight in the jungle (Guerilla Warfare).
Groups that were against the war were the Australia Labour Party, trade unions, Save Our Sons and etc.