Ok I'm your man! First things first, STAY OUT OF THE BIG CITIES. You want to go to Queensland, so I'd take the Qantas Los Angeles to Brisbane flight. Once in Brisbane, spend a day or two and check out the sights around Queens Street, if you wish. It might be a good opportunity to gauge what people are like in Australia. Now here's the good part. GET OUT OF THE CITY and take a bus ride into the Outback, it will blow your mind away! Whatever you do, you have to go traveling through the Outback, it is not like any road trip you will ever take in America. Take a tour on a ranch or farm, I did one near Roma on one called Telco I think. You will see a lot of nature...hawks attacking goats and joeys, herds of kangaroos, wallabies. Around the Glass House Mountains is Steve Irwin's zoo, that's definitely worth a visit. The coolest part of a trip there are the Tasmanian Devils, they are hilarious. There are some huge crocs, koalas and whatnot there, pretty cool.
I would arrange to spend most of my time in the Outback, the cities are awfully boring. I heard Sydney isn't that much better. I would say going to the Outback was definitely one of the best things I've ever done in my life. Take a chance to talk with some of the locals, they are very friendly and open, unlike American people. They have lots of good stories. Take a few snacks that you will miss during your trip, what you get there will definitely be nasty. Beware, the food there can be disgusting at times. The products in the grocery store will seem like a joke the first time you go. Most of the burgers I had were pure garbage. I had the worst pizza of my life at a Domino's there. Be polite when you eat homecooked meals there; most times they will be disgusting and bland. Just a head's up!
Oh, whenever you get in, remember that most stores and places close by 5 or 7 pm. So if you need anything before you rest after that awful 14 hour+ flight, get it before then.
Tipping is not expected there btw, believe it or not. Do it anyway if you really like the service, most people are really nice there.
I forgot to mention, Cairns is supposed to be nice and tropical too. Most Aussies told us visiting Sydney was pointless, some Americans told us that too.