Well, we're from the U.S. but we've done 2 four week trips with our kids in the last six years and then we'd gone before without them.... If you will be in Melbourne, investigate the Great Ocean Road. We drove it once, we didn't have plans to go off it but I saw signs for a lighthouse and we decided to take it, well, we got lost on the road (it was small so we weren't so lost) and found ourselves in koala heaven, there were hundreds of them hanging from the tree's above our heads! The most fascinating thing ever... then we stopped at one of the stops on the road with no particular purpose and saw the smallest marsupial, my husband thought it was a rat, I said no, it mustn't be as it was hopping like a kangaroo would.. there was an Aussie there who said he'd been driving the road for 7 years and had never been fortunate to see one until that moment. Another fascinating moment.
Kangaroo Island is FANTASTIC to see wildlife. (It's a flight from Melbourne or Adelaide) We stayed at a cabin/campground (we stayed in the cabin) and daily we had kangaroo's around us (among other critters)... you must be careful not to hit the kangaroos or other animals however, so it's a slow go, but totally worth the trip. You can fly or drive from Melbourne, in fact you can take the GOR much of the way to Adelaide (which we did). If you have time drive through the Grampian Mountain Range, perhaps stay a night.
We've been to Sydney so often now that we only stay for a few nights, eat at our favorite restaurant and move on... but a cruise on the Harbour and the Opera House are beautiful and the zoo is really quite good there. It's not to be missed. There is much to see and do in Sydney, so many different sections of the city. With time in mind I'd stick to the main attractions and move on. Since you will be there during the cooler months I would suggest a visit to the Blue Mountains if you have time.
I'm in the minority, we love Brisbane and we never miss it, we visit a themepark called DreamWorld that is so fascinating... there are rides (good ones) but then there is a completely different side where you visit all the animals. Each part of Australia is represented there, you walk among the kangaroo's. Last we were there you could still hold a koala, although I understand the rules surrounding that might have changed. If you are making this a once in a lifetime trip take a trip over to Moreton Island to stay the night at Tangalooma Resort and feed the wild dolphins. That was a wonderful experience. The accommodations aren't what we are accustomed to, but the experience is priceless... Once we visit the city and the beaches we move up to a place called Noosa, it's a gem of a vacation destination and one that foreigner's often don't visit. You can ride camel's on Rainbow Beach and pretty much relax and have a wonderful time exploring the area.
We have also been to Cairn's without the kids, although we have not been during the months you are going. I can recommend a wonderful place to stay (Kewarra Beach Resort). You must take a tour of the Great Barrier Reef.
We have been to Alice Springs and Ayer's Rock, too bad they have implemented a speed limit between the two places
but, if time were a concern, this is one stop I wouldn't make. It was nice, we liked it, but with younger children they really couldn't appreciate it. This is a trip best kept for the adults IMHO...
I would never go through a tour operator that schedules every activity. Sometimes you can save money by purchasing a tour through Qantas that includes a certain number of stops in the country and that can work out well, but the one thing we have learned in Australia is that the most exciting experiences we've had were the ones we never planned on. We still have to go back and bring the kids to Cairns/Port Douglas, Darwin and Perth as they have never been (and I want to drive to Monkey Mia from Perth), that's another 4 week trip but should round out all the places we have yet to visit with the kids
Once you go to Oz you never stop... Whatever you do, wherever you stay, have a wonderful time while you are there! And, in fact you might get some skiing in, although as someone said it will be expensive.
I just saw your last question... for us the best zoo was everywhere
If I was limited I would go to the Sydney Zoo, but I like Dreamworld for it's zoo you get so up close and personal. There are a couple of low cost air carriers in AU, so I think we booked our internal travel anywhere from 79 to 139.00 AU but we watched the flights for quite a long time waiting for sales. We went during their summer/school vacations, I bet the off season would be even better.
or we saw a lot of "wicked campers" on the road in QLD - these look like basic "hippy campers" or converted vans, with just a bed in the back, they are painted up graffiti style - there were heaps of them, so there must be a firm hiring them out somewhere. It was a game of ours to spot the wicked camper. Not my idea of a family holiday, would be fun for a couple of young hippys as long as the weather was good, but each to their own 
but I do owe you some good advice! 
So much to do and of course so little time! We are from Ballarat area and can completely back up the previous recommendations of the Great Ocean Road, Ballarat Wildlife Park and my own personal favourite Sovereign Hill. 
(I really can't resist this one)......The Sydney $? 
