I'm sure it would be legal in Australia to buy a scanner to listen to the aviation band. If you want one that transmits you will probably need a license to operate it if not buy it, but then you really don't want to be transmitting anyway.
Personally I would not think it's worth the money. Listening can be interesting but it gets old quickly and you don't learn as much as you might expect - RT work makes more sense in context. My personal experience is that the hard part of RT is not knowing what to say but getting it out in the cockpit when you are also flying and navigating as the same time, and that only comes with experience.
If you are taking lessons why not ask if you can borrow a handheld radio from your training organization? They probably have one or two lying around.