Which book should I study to learning flying in Australia?
CASA (the Civil Aviation Safety Authority) has a number of resources that might be of interest, in fact a lot of their safety publications and videos are as good as (or better than) the FAA equivalents. As best I can tell they don't have anything equivalent to the textbook-level Airplane Flying Handbook or Instrument Procedures Handbook from the FAA though.

You can find references to the FAA handbooks in some of CASA's CAAPs - for example, the Night VFR Rating information references the Airplane Flying Handbook's section on Night Operations) - so clearly they consider at least some of the information broadly transferrable. 

Like Farhan mentioned the operating principles, maneuvers, etc. are going to be largely the same because the plane doesn't care what country it's in. It's the specific regulations (and regulatory citations), airspace design specifics, etc. that will vary but if you're aware of that you can easily pick out the parts that you should pay attention to versus the parts you'll need to go and cross-check in an appropriate Australian reference like the Part 61 Manual of Standards for flight training / practical test requirements.