SemiElite is right--Go for F. Much better product and just a few more miles needed.

Having done QF awards in F and C, my suggestion for finding availability is this:

Enroll in the QF frequent flyer program, so you can check availability online at qantas.com. The key flights are the tranpac ones--so search those first and by themselves.

NOTE: The CO OnePass and AA reward ticket inventory is not exactly the same as what you see on the QF website for redemption of QF miles, but I can tell you from experience that what you see is pretty darned close so it is a good place to start and the free seat you see if probably available for you using CO or AA mileage.

Good luck.