Hi Mal, I would imagine that there would be a lot of Western Bearded Dragons (Pogona minor minor) available from breeders and pet shops alike. They are easy to source in Perth. You will need to hold a category 2 reptile keeping licence to be able to purchase and own one. They do require heating, roughly 35-45°C for the hot spot. I suggest reading A Guide to . . . Australian Lizards in Captivity by Dr Danny Brown or Keeping and Breeding Australian Lizards edited by Mike Swan. They are considered to be easy pet lizards to keep, although the wild caught ones can be finicky so make sure you select one that is captive bred and feeding well.
It is key to do your research in selecting the species of lizard that would best suite your requirements. Are there other lizards you are interested in that you are allowed to keep? What in particular are you looking for within a pet lizard? Does it have to be pretty? Small? Handable? Blue-tongues and Bobtails/Shinglebacks are good pet lizards, if not on the large size. Centralian Blue Tongues (Tiliqua multifasciata) are the smallest Blue-tongues that can be kept in WA. I'm not much of a gecko expert nor avid keeper of them, however. I currently keep some Three Lined Knob Tailed Geckos (Neprurus levis pilbarensis) but I will be getting out of them shortly, they require heating, roughly 30-32°C for the hot spot. Think carefully on your choice. I hope this helps you.