Hi Happy
First thing I'd do is take a few trial lessons at your local school. This gives you the chance to firm up the decision of wanting to fly, as many people, after their first flight decide to be sick or hate the idea! After that, you'll need a medical exam, which is vital. After getting this, it enables you to undertake training to become an airline pilot.
Consider your age. You may be elegible for sponsorship should there be anyone out there sponsoring. If you're out of limits for that, then the only way is either burning all your cash on an integrated course (which is what you probably had a preview of at the flying school you mention), or progressivley gaining the necessary tickets and experience, to end up with an ATPL (or is it ATP over there?).
Finally, have a talk with current pilots to see how they did it in Australia, and discover how much more than flying there is to becoming an airline pilot! Some people like to call airline pilots "Panel Operators" or "Systems Manager" as basically, except for the first and last few minutes of the flight, that is what you are doing, though this is depending on what kind of piloting career you are after. (Another important thing to consider, which could alter your training regime).
Good luck in the future!
obk.
