Fair Work Australia
You need to do 3 things.
1) Keep PROOF of hours worked. If there is no documentary proof in the form of payslips (which employers are legally obliged to give you, by the way) then make your ownproof in the form of a work diary including start / finish times, dates, flights etc.
2) Leave.
3) Go to fair work australia. Even if you are a contractor, there are provisions in the award for casual employee rates. In any case if your employment is more in the nature of an actual employee rather than a contractor, FWA may determine that you should be entitled to (some) entitlements of an employee. Google search "Sham contracting". I dont know the details of your employment so this may or may not apply to you.
BTW if you are employed as casual you are supposed to be rostered for a minimum 2 hours flying per shift according to the award, IIRC (dont have it in front of me atm, so you'll need to check).
As for some of the previous comments about 'doing the hard yards' in various other walks of life.. this is absolutely irrelevant. Employers either pay the award or they packup and go to some other dodgy backwater. This is legal minimum entitlements we are talking about here, not some kind of generous wage. We ALL have a right to be rewarded at a minimium level for our work, such that we can at least afford to live.