Most major companies out of Brisbane (and most capitals except Darwin) have unlimited mileage, just check the fine print as a few smaller ones dont. It is not likely to change the next few years.
Another way to do it on a budget is to find a "relocation" rental, this is when cars/campervans are needed to be taken from location to location, often it can be for $1 per day with a fuel allowance, but the time can be restrictive.
Just remember Australia drives on the correct side if the road and have decent insurance as the excess is about AUD$4000 for an accident.
Cheers
FF