In the period when the lush ancient forests exited on Earth, the ones that provided the material for the formation of the coal that we use nowadays, Australia did not provide the right conditions for the existence of these forests.
The problem was that Australia was located very close to the South Pole in that period. Because of its location, Australia was colder and drier than most of the landmass on the Earth. By having less precipitation, and colder climate, Australia was not suitable for the tropical rainforests of that period, thus it did not had the material from which the coal formed latter on in the geological time scale.