Australia is the arid continent. The principal features of Australia's climate stem from its position, shape, and size. There are two climatic zones: the tropical zone (in the north above the Tropic of Capricorn) and the temperate zone. The tropical zone (consisting of 40% of Australia) has two seasons, summer (’wet’) and winter (’dry’), while the temperate zone has all four seasons.
Because of its relatively low latitudinal position, Australia comes under the influence of the southeast trade winds in the north and the westerlies in the south. Northern Australia is affected by a northerly monsoon, partly because of the latitude and the seasonal migration of planetary wind zones and partly because of the summer heating of the continental interior that draws in surface winds.
Summer (December to February) can get uncomfortably hot just about anywhere, even in Tasmania. If you're in the southern states during these months it's great beach weather and great melanoma weather. Up north, this is the wet season, and it's very, very humid.
Overall, spring and autumn are probably the safest bets - the weather is reasonably mild wherever you are, and spring brings out the wildflowers in the outback, while autumn is particularly beautiful around Canberra and in the Victorian Alps.