Hello Kimberley and welcome to Travelblog!
As a resident of Brisbane for nearly 20 years, I can certainly comment on the Brisbane side of things.
Firstly, weather - Brisbane is a subtropical climate, so winters are mild and usually dry (though we had a wet winter last year). Days usually don't get much cooler than 20 Celsius (68 Fahrenheit) but they can drop down to lows of 15 Celsius (59 Fahrenheit) on what is termed here as "cold days". Nights sometime drop into single figures (below 50 Fahrenheit). The worst month here is typically August, because that is when the westerly winds blow in, and it usually is quite uncomfortable for a few weeks. Other than that, the weather is glorious here at that time of year.
There is a lot of public transport around, but be warned, it is not cheap. In order to save as much as possible purchase the public transport Go Card, you can recharge, and fares are much cheaper if using it. The bus network in Brisbane is extensive, trains less so and ferrys/CityCats only loiter on the river (obviously!).
Australian cities are large sprawling affairs with lots of space, so if you can try to get nearer to the CBD (Downtown) area, otherwise you will have a long commute to get anywhere.
Two final thoughts, at the end of August/early September is the annual River Festival in Brisbane, and it is the best time of the year to be here. You must try to catch the annual Riverfire, it is well worth seeing.
Finally, budget extra for food. Australia is one of the most expensive places in the world to shop for groceries and food supplies - even more than Scandinavian Europe according to friends who hail from that part of the world. Almost every visitor from overseas who I've met through places such as Couchsurfing comment on the high cost.
If you have any further questions, please post again.
[Edited: 2012 Mar 30 02:22 - The Travel Camel:11053 ]