June / July will be off season, winter (which is not winter like here in the US). Therefore, you should be watching for fare sales as it's gets closer, I wouldn't suggest arranging now unless you are trying to use airline miles? 2 weeks should be a minimum stay, it's a L O N G flight. Brisbane is wonderful, Steve Irwins zoo is top notch. Sydney is without saying one of the most beautiful cities on Earth. You'll want an Australian airline flight between the 2 cities, it's quite far. Think about cell phone coverage, do your plan(s) have any there, what does it cost, what do you need, does the same number matter, etc.
Cheaper Australian airlines include Jetstar, Virgin Australia, Tiger Air, you should get on the mailing list for those to get announced fare deals to save money, there is a lot of time for that and you will find some great sales.
Australians do drive on the left side (unlike the USA), so, get ready for that if you decide to rent.
Brisbane has a lot of potential tours into some of the outback, or even jungle.
If you want to do something less urban, consider Palm Cove area, some TS there and a lot of activity with the Great Barrier Reef, night zoos (a blast!), and many other things. You can surely exchange into some in that area with your TS.
Been a while since I went to those 2 cities admittedly. Was just in Melbourne, Perth, and, Busselton last year. I have a friend who lives in Melbourne.
You will enjoy the trip! Australians are mostly very friendly, and, while they speak English, it's sort of fun learning hundreds of new words!
If you like Fizzers, try Fruit Tingles while you are there, always been addicted to them.
Do you have any specific questions? Open ended is kind of hard to respond to.