An oldy... but a goody !!! Travel depends on where your going, it's a huge country !!!!!! Travelling from East to West, I'd go between August & December, down south, anytime but obviously winter is a lot colder but no snow except in the alpine regions which are small .Right up north you don't travel during the wet season which, i think, is between december & april.
If you've got some place in mind post it here & all us Aussies will let you know the best time & things not to miss !!
........................MIck