Neither. Quite simply.
The Australian political spectrum throughout the Cold War proved inhospitable to either the far left or far right.
Avoiding the hyperbole of various wingnuts about person x,y,z of being fascists/communist, and whether certain individuals were communist agents or 'fellow travellers' of the cause, its nigh on impossible for Australia to be turned into a communist state, even if individuals who were of a communist bent were able to gain the highest office (through a Labor electoral victory), but that would prove pretty impossible as well as the party split over far left influence (amongst many other things) in '55.