i think you have to apply for a visa as you would to visit the states. You'll need to submit the reason for going, date returning, details of your conviction etc.
They will consider it and reply within about 2 months. It does take ages so you'll need to allow plenty of time.
For quiet a number of years the only visitors to Australia went as guests of the HM government... all chained together, wouldn't worry TOO MUCH If'n I woz you Sheila....!!