For me for future reference…
OK, here’s the deal with an international Qantas connection at LAX from a domestic American Airlines flight. If you have an onward boarding pass for a QF flight (and on a single ticket for both the AA and QF flights?), and take the shuttle at Gate 44 in Terminal 4 to Tom Bradley International Terminal TBIT, you are already airside and DON’T have to go through security again at TBIT.
Unfortunately, this Qantas webpage (http://www.qantas.com.au/travel/airlines/airport-guide-los-angeles/global/en#transfers) is not clear about the security thing and I had to spend 15+ mins on the phone to Qantas to find out. The webpage implies that you don’t have to go through security again but it doesn’t say so explicitly. (The first highlight below explicitly tells you about security, but the second highlight doesn’t — it’s implied that you don’t have to, but I wasn’t sure.)
Thanks also to friends who do this connection regularly who also told me that you didn’t have to clear security again. It’s now been confirmed by Qantas.
BTW, the Qantas person I spoke to said the shuttle ran every 7 minutes.