+1 for not trying to do too much.
And +1 for taking into account the weather in deciding where to visit.
If you had 1 month to 'see' Europe you would similarly miss a lot out, so try and work out what you really want to see and do. I would highly recommend hiring a car + take camping gear or hire a campervan to get out of the cities to really appreciate the landscape and wildlife. (We paid ~AUS$1000 for 2 weeks campervan hire, one way between Melbourne and Brisbane - which was a bit too far really, but we had cheap flights! - plus about ~AUS$15-30 per night for campsites back in 2010). You wouldn't need to book campsites ahead at that time of year (we arrived at a Blue Mountains campsite that the guide books say fills up months in advance, at the end of Feb, and we were one of only three couples there).
Whereas if you are going to fly in and out of 4-6 different cities, then it is probably worth booking a vacation rental and doing day visits from each city. Depends on your personal preference.
I think you get more for your money with a vacation rental, if you are staying in the same place for long enough. But thats just my opinion!
For koalas on the GOR I would add Kennett River to mikewsmith's suggestion. Kangaroos and wallabies can be seen all over once you get off the highways; we saw most variety on the back roads but they disappear into the bush pretty quickly. Also, if you head towards Adelaide, Kangaroo Island is supposed to be great for wildlife and star gazing. And there is a very large penguin colony on Phillip Island near Melbourne if you have never seen them in the wild, very cute (though you can also find lots of penguin colonies in Tasmania and NZ).