As a Brisbanite for the last 5 years I would recommend it. As you say, the weather is a big factor there although at this time of year the humidity can get a little overwhelming.
It's only about a hour and a half train trip down the the gold coast, where the beaches are amazing and there's plenty to do, and a bit longer up to the good beaches in the sunshine coast as well which is a bit quieter but just as nice.
You can also get up to the glasshouse mountains (near the sunshine coast) for some great hikes, and down to places like mt tambourine and byron bay without too much travelling. and there are also some great islands just off the coast, like stradbroke, moreton and fraser, that have some really worthwhile places to visit and hike in.
and depending what sort of accommodation you're after you could do it much cheaper than $100 a week. take a look around one of the uni's (uq or qut) to do the sharehouse thing for heaps cheaper. of course it depends on how close to the city you are. its a good idea to try and get a place somewhere on the train line, cos then you can get around really easily and get to most of the interesting places even if u aren't living right in the centre of it.