I am Australian and I hope I can help.
Firstly, you don't need to fly through a university. There are hundreds of private flight schools here which are of great quality, and very few of them are associated with a university. More and more international airlines are sending cadet pilots to our schools. Most of them offer theory courses in addition to the flying, or you can always self study.
Having said that, the university courses are great and airlines like people with a degree (but it's not mandatory to have one). You'll be paying more though, it's a trade-off.
Your comment about small planes - All flying is initially in light aircraft - even if you got an airline cadetship you start small. No single course in Australia or anywhere will let your first flight be in a jet.
Speaking of airline cadetships - these are definitely the best and quickest way to get into an airline cockpit but the positions are highly competitive (and maybe not open to international students, I don't know). But you can still get an airline job without a cadetship...
The normal progression is this - you can technically get a flying job after 150-200 hours of private training and flying, having achieved your commercial pilot licence (CPL). I say 'technically' because if you only have minimum hours and minimum qualifications you have to look very hard for a job. Most people straight away get an instructor rating, so they can get a job teaching people to fly. Other early jobs include sightseeing flights, parachute flights, and mail flights to remote towns.
Your training will have been in light aircraft, but fortunately Australia has possibly the largest light aircraft industry in the world, so there's lots of jobs in these planes. It's highly unlikely that your first job will be in anything bigger than a 6 seater plane.
If you get extra qualifications (such as multi-engine endorsement, and instrument rating), you can get more jobs, and gradually fly bigger aircraft.
After you have your CPL, the next big step is the Air Transport Pilot Licence (ATPL). Regional airlines here generally require as a minimum, 1000 flying hours in light aircraft, the multi engine rating, the instrument rating, and passes in the ATPL theory exams - note that you don't necessarily need the ATPL licence itself. It will take most people a couple of years until they get this experience.
If you have that much experience flying 6 to 8 seat aircraft, it's not actually a huge leap to the 20 seat planes of the regional airlines, and the airlines will train you for this step. And once you've flown those for long enough any airline can train you to their jet.
Of course if you want to go back home after the training it will be different. But no school here can train anyone to go straight to an airline. You've got to do the small things first. Think of it as character building!
I'm sorry but I'm a bit rushed for time but I hope I've helped a bit. Australia is one of the best places in the world to train in my opinion (but I might be biased!). Please ask if you have any more questions. And good luck.