dave's the real expert, but I'll share some tips with you from my travel around Australia:
It's rainy season in the tropics. Not that nice gentle rain you have everyday in Singapore either. It can bucket down, ruining everything you planned to do.
I'd opt for Brisbane and Sydney, plus Hunter Valley while in Sydney. I know you love red wines and the Hunter is huge for nice reds. Also since it's away from the city, you can easily rent a car in Sydney and drive there, seeing lots of countryside while on the drive. Also staying in Hunter Valley overnight is a nice option. Several of the wineries have accommodation which are a real treat. Some offer dining as well and there are many other options for dining in the Hunter. The Hunter Valley is fairly remote from any large city.
And, although you've seen large cities, you've never seen one like Sydney, especially the harbour and the quay. A very nice getaway from Sydney is a harbour cruise to Manly for the day. Once you're off the boat you can walk the entire Manly area, dine on the beach, enjoy the warm day, then travel back through the harbour at sundown and see the sunset over the city. It's remarkable day.
There are several national parks around Sydney where hiking is excellent. Plus, there is the Bondi to Bronte beach walk and other city/seaside walks as well.
The key to having a good time in Sydney is to stay near the Quay.
Seeing the Gold Coast while in Brisbane is a definite option for more beach time. It's lovely at Main Beach and Surfer's which are at the north end of the Gold Coast, making those beaches closer to Brisbane. In Brisbane there is plenty to do for a couple of days of sightseeing.
John and I want to share a meal with you two, and we'll also be available for transportation in and around Brisbane. And, of course, you're welcome in Redcliffe where we live. It's very nice there on warm weekends. We have a cafe strip, an open market, swimming, and Sunday session at Mon Komo, the hotel on the cafe strip.
Actually, you can't oversell Australia. It's a wonderful as the photos suggest and as everyone says it is. It really is paradise. Once you've seen Brisbane and Sydney (and I know you've already seen Perth), you will want to come back for Melbourne and Adelaide, two more fabulous Australia cities.