When you land at LAX, you will arrive at Term 4 (AA's terminal). Qantas uses TBIT. You should not have to pick up your baggage at LAX and recheck it - so you will only need to worry about getting yourself over to TBIT.

In the evenings, there is a shuttle bus from Term 4 for passengers connecting to Qantas, leaves ever 30 minutes. It leaves from one of the Gates in Term 4. If you are able to use this shuttle, you won't have to reclear security at TBIT.

If for some reason you arrive and the shuttle is not running, then what you will need to do is exit the terminal, and then when you get outside, walk to the left on the sidewalk - takes 5 minutes at most - and you will be at TBIT. You will then need to reclear security.