The closest thing to a Leopard Gecko in Australia in terms of size, how you keep it and how well it handles is probably the Joy Lizard or Knob-tailed Gecko, Nephurus levis (what you have pictured on the left are Joy Lizards). They come in lots of colours and are very easy to keep. By Australian standards they're a very large gecko.
They've been very popular lately and get snapped up quickly, but if you keep your eye on the classifieds you should be able to find some before too long
There are also plenty of climbing geckoes, some of the Oedura species are good, and if you want something smaller you could go for a Diplodactylus (these don't climb much) or Strophrurus (like your picture on the right). Plenty of wonderful Australian geckoes to chose from