pet lizards

Question
what types of lizards can you have as pets i live in australia so i dont know and can you get vegetarian ones.
I also want to name my lizard bobby jo. also do lizards breed like rabbits.

Answer
 Australian laws regarding reptiles as pets, native and imported, are rather strict and strictly enforced, although they have (foolishly) opened discussion on importing bearded dragons that have been raised outside Australia primarily for the pet trade.  I say foolishly, because the limited gene pool has made a sicklier, smaller specimen that may have a very bad retrovirus called adenovirus that may decimate the wild populations in your country if any should escape.
 There are vegetarians in the iguanid species and the uromastyx.  Uros, of course, though needing higher temperatures, are smaller and easier to handle than iguanas and cyclura.