QF is NOT impossible. You need to book 11 months out. The drill is to open a QF FF account. Ths gives you the opportunity to search the QF site for available award seats. I have gotten a JFK-LAX-MEL-SYD-LAX-JFK FC ticket, as have many others. You just need to play the game properly. About a week ago I was on that site looking for something to Oz next Labor Day and found FC seats to MEL available. So they are there, you just need to remember that you are competing for very few sets with QF, AA, US, CO and probably other FFs.
But, it can be done.