Welcome to InsideFlyer! It really depends which part you want to go to - this is a pretty good introduction: http://www.travelandleisure.com/travel-tips/best-time-to-visit-australia In general, I try to avoid places during the real peak months (which tend to be busier and more expensive) and go a little before or after instead - 'shoulder season'.
All year round if you go to the main cities, if you want to travel North then go May to October - the dry season
