Brisbane is a nice city, possibly the nicest large city in Australia. But it's bloody steamy at that time of year, and still a city.
Hire a car and drive out to Toowoomba - that's about 2 hours, a little less. In the evening, go to the Weiss restraunt on the hill on the edge of town. Order Moreton Bay bugs (a sort of crab/crayfish thing that is absolutely the best seafood you will ever eat). Drink some of the second-best beer in the universe (i.e., XXXX, which is pronounced "four-ex" because Queenslanders can't spell "beer"). Eat some more bugs.
If you can still walk, go back to your motel and sleep it off.
In the morning, continue to the Bunya Mountains. Delight in the cool mountain breezes and the astonishingly peaceful scenery.
This fellow will eat out of your hand:
As will various of his friends of many different species, and the lush green lawns of Bunya are alive with wallabies. You'll stay there all day, delighting in the relative cool and the peaceful atmosphere, maby stay there that night too.
Next day, you can return the way you came, or (better) continue north, travelling through the rich, rolling peanut country around Kingaroy, and veering right to head eastwards to meet the sea. That brings you to the Sunshine Coast, which is vastly nicer than the horrible neon-ridden Gold Coast south of Brisbane, and will give you the chance for a swim. (Can you swim there in summer? I think so. Further north you can't swim in the summer months because of the deadly Box Jellyfish, but I don't think they come as far south as that. Don't worry about it: if there is any danger at all, there will be signs and thingsa all over the place. Queenslanders take water safety seriously.
If you have an extra day or two to spare, at the northern-most extremity of your trip, you are only 80-odd kilometres from Hervey Bay, and from Hervey Bay (or Bundaberg) you can take a short trip by twin-engined light aircraft to one of the most wonderful places on the entire Great Barrier Reef:
Lady Elliot Island. You can day-trip there, but much,
much better to stay a night or two. As these things go, it's not expensive, and you can spend your days in a wonderland of warm, crystal-clear water getting as close to the coral and the fish as you like (no need for scuba gear at Lady Elliot, the schnorkelling is superb), and the early mornings and the evenings eating tropical fruit and fresh-caught fish (all provided for you) while you watch the thousands upon thousands of stunningly beautiful pelagic seabirds coming in to their nests to feed their youngsters.