For essentially the same reasons as the US did. They had provided assistance to the South Vietnamese government in the way of military 'advisors' but now they wanted to extend that as the conflict expanded.

Robert Menzies said in the speech announcing it "The takeover of South Vietnam would be a direct military threat to Australia and all the countries of South and South-East Asia. "

Australia was (and is) linked heavily to US foreign policies and mainly 'rubberbands' its actions to those of the US. Thus the 'Red threat' and the idea of a cascade of communist takeovers of the world was seen as a real and genuine threat. Its highly unlikely to be seen as a realistic threat now, in retrospect, but back then it was.

Australia is fairly conservative on foreign affairs matters and, protected and supported by the US, hasnt shirked from various 'expeditionary' activities to support the anglophone-based West policies. Some would suggest that since the end of WW2 Australia has essentially acted as a technically-independent but inextricably linked arm of US Foreign Policies and subsequent military actions. New Zealand followed a similar path but during the 70s and 80s its anti-nuclear stance separated it somewhat from its ANZUS allies.