Well I fly a lot and have the system down.
If you are do in at 6am the Customs lines won't be bad. Get in an hour later and the lines start to double in size. You probably know your going to have to pose for a photo and get that digital finger print.
If you purchase any duty free liquids and carry those onto your Qantas flight, you will have to put them in your checked baggage in LA. The rules on liquids at LAX should be the same as they are when you leave Australia. Thats bottles no larger than 3 ozs, and all of those 3 oz bottles must fit into a 1 quart bag. Only one 1 quart bag per person.
While in Oz we discovered that your post sells some really nice wine bottle packaging which we used to place some wine into our checked baggage. Of course the TSA here went through those bags a couple of times, but the wine made it just fine. The rest of the bag was a mess ...but hey the important stuff made it
It was bad flying Qantas out of LA back in 2002 when they were still flying out of the international terminal. That terminal is tough - the phrase "train wreck" would apply if you had to use that one.
You may have an issue when you land with your checked baggage. All of our airlines have differing rules on accepting or transferring baggage based on your layover time. As long as Qantas prints the connection info on your baggage tags you will be fine. There is a re-check station right as you exit customs.
If Qantas doesn't print your connection flight info then you have to go to the airline counter and try to check it. But thats a 12 hour layover - I am guessing you will have to keep your baggage for a while. If that is the case, I doubt you will be able to get back into the terminal as they won't let you through the security check point.
If you are going to try and catch an earlier flight, you would have to keep your baggage anyway as they really don't like to spend the time searching for baggage to change the tags and flights. Also many (not all) flights these days here are close to sold out or over sold. It is not like it used to be when trying get on a different flight. If you are using FF miles, be prepared to pay a change fee as there isn't anything free on free tickets anymore.
Oh and the airlines here are not completely like crapstar. It's not $7.00@kilo it's usually a flat $50.00 for over weight bags. But the baggage allowance is a bit higher here. (1 kilo = 2.2 lbs). No real food to speak of on our airlines - but coffee, tea, soda etc is free.
Hope your flight goes well - sorry your not going to make it to Florida
Cheers
Steve and Andrea