If you use a revenu ticket rather then award ticket using QF for LAX-SYD, be careful that you get an AA code share QF flight or check to see if your QF fare class are 1 Miles or .5 miles on AAdvantage.
Have not flown Qantas from US to Australia but have don NZ to Australia and coach for the 14-15 hours would be brutal for someone who is 6'6"..
Mary