Australia's seasons are reversed from the Northern Hemisphere, and the continent is big enough that the "best time" varies dramatically by region.
Broadly, the shoulder seasons — March to May (autumn) and September to November (spring) — offer the best balance of pleasant weather, manageable crowds, and reasonable prices across most of the country.
The south (Sydney, Melbourne, Adelaide, Perth, Tasmania): Summer (December to February) is hot and popular. Sydney and Melbourne hit the mid-30s°C regularly; bush fire risk is real in rural areas. Autumn and spring are ideal. Winter (June–August) is mild — rarely cold — and much quieter, with lower prices.
The north (Darwin, Cairns, the Kimberley, Kakadu): The year divides into two seasons. The dry season (May to September) is the time to visit: warm, sunny, and accessible. The wet season (October to April) brings intense monsoon rains and flooding that can close roads and make the Outback impassable. Humidity is oppressive, and some national parks become unreachable. Kakadu in the dry season is exceptional; during the wet, you may not be able to get there at all.
The Red Centre (Uluru, Alice Springs): Avoid summer — daytime temperatures regularly exceed 45°C. The desert winter (June–August) is spectacular but can be surprisingly cold at night, dropping near freezing. Spring (September–October) and autumn (March–April) are the sweet spots.
Tasmania: Summer is the best time — long, warm days and (relatively) little rain. Winter is cold and wet but the island remains open and the scenery is dramatic.
The most expensive period to travel is December to January (school holidays, Christmas), particularly in coastal destinations. Book well ahead if visiting during this window.