It is important to check with the airline. Qantas does use both the American terminal 4 and the Bradley terminal. I am on QF 26 ticketed as AA 7337 leaving on 11 27 07 that leaves at 8:30pm and am told it leaves from the Bradley International Terminal.

I would suggest doing a google search for LAX and looking at the map to decide if the walk makes sense. There are shuttle buses that will take you from one terminal to another. LAX is a U shape with T 1 starting at the lower right. Bradley is at the top of the U.