I presume Australia has the same kind of system the UK does.
I think the parlimentry democracy system works pretty well, although since Thatcher the prime minister has more power as an individual than ever before, I don't know wheather Australia is in a similar position. In the past he/she was more of a spokesman for the leading party as a whole.
A republic would only increase the power of an individual 'head' of state, but I think it should be partys that have the power, not a president.