The Motorcycle Australia (MA) website is a good starting point for information on licensing because it highlights how you can apply for a race licence (from MA) which is required to go racing and also provides a snapshot of state based licensing requirements. To assist there are also has links to the various state authorities, which is important because not all States treat Learner Approved Motorcycles (LAMs) the same.
Learner Approved Motorcycles can be ridden by learners in most states (but not in WA currently). These are motorcycles up to 660cc capacity and a power to weight ratio not exceeding 150 kilowatts per tonne.
Visit the Motorcycling Australia website for an overview and more information.
Or visit the following websites for state licensing authorities in your State: