Pete,
I agree with the sentiments of the others here for a number of reasons.
1. Qantas do not require one at the moment but a) it may change and: b) it can't hurt your chances. It may also enhance your chances of a management position at a later date.
2. If you don't get into QF (and I won't go into the whys and wherefors about that!!), if you go to the US looking for either airline or corporate flying, a degree is almost a neccessity and I think many of the Asian carriers look upon a degree favouably.
3. If you have to give up flying for whatever reason in the future, again the degree may open up other avenues to you.
Furthermore, I agree with JT's view that you are better doing a general degree rather than an aviation-specific one since an aviation-specific one may raise eyebrows outside of the industry and conversely a general degre is, by its very nature broad but still very applicable to the aviation enviroment. I would suggest a business degree such as a B.Bus, B.Comm or BEc. (I must confess though, to being biased here, I have a BEc.) Additionally, HR types will be familiar with them, and they seem to hold sway these days.
Another suggestion (bound to upset some) is to be careful of the degree and the institution as some degrees are of the Mickey Mouse variety designed more to produce fees for the Faculty offering them, rather than any serious academic pursuit.
Personally, I would be very wary of Grad. Dips that don't require an undergraduate degree as a prerequesite.
Good luck!