Rabbits breed like anything though, agreed so do guinea pigs. But I don't see how a handful of hedgehogs/degus/chinchillas would ever be able to over populate and become out of hand some how. There's probably way to many things that would eat them before they could achieve world (Australia) domination. I don't think I could live in a world with none of those animals and a ridiculous amount of spiders. How do you cope?!
However, I agree I've learnt so much about Australia and their animal laws now! How interesting