Sounds like you may be in LAX heading back to Australia, but you don't say for sure where you're going.
If BNE then you fly out of the AA terminal 4. The Admirals club will be your lounge if you are SG & in Y or J. This is a pleasant space to hang out in, with food for purchase & a voucher will be given to you for alcohol. Other beverages are free. Simple cold nibbles are also free. IIRC there are showers. If WP or F then within the Admirals Club you will be given a key card to the Flagship Lounge. This is quite nice with showers, hot & cold food selections & a good selection of grog, all in the same style as the QP ie help yourself & free with the ticket / status. Can't recall if they call the flights. Ask at the desk.
If you are heading for SYD or MEL, then you will be in TBIT. The lounges are on the 5th floor, with the J/F lounge to the right of the QP. They share showers. Both are more the style of the DOM lounges in Australia. Hot & cold food, good selection of non& alcoholic beverages. All help yourself. The J/f lounge is not like the F lounges in SYD / MEL. They call the flights, so you can relax & enjoy right until the mass exodus.
Personally I prefer the Flagship lounge in Terminal 4, but it takes time to catch the airside bus from T4 to TBIT airside ( if it is still running with the renos going on), allow at least 30 minutes.
If you are flying into LAX on AA, your only chance could be to have a printout of your QF Summary showing HM SC you need to get to WP, then go into the lounge with your BP & Summary & do a show & tell. I find the agents have more time there. You could do the same show & tell at TBIT lounge too. They may say no because really it is up to QF to progress you to the next level, even if you have qualified.
It would be nice for you to enjoy the differences between the lounges seeing you are there, so worth a try. Biggest difference to you will be if you fly out of Terminal 4.
If you can only access the Admirals Club part of the lounge, others here have been successful in asking for more than one drinks voucher. Getting the drink from the barman, I either don't tip, but then often feel cheap, or I tip $1 or a few quarters. Wages are not the same there. Others here will have their own opinion on tipping, but that's what I do. When in Rome...
Edit: Spent too long typing - Kangol beat me to some of the info!