Depending on what the roadwork behind the airport is like, you could do a run down lomandra rd and sugarmill road. couple of roundabouts to drift. It's not an exciting run, but it's the only thing out that way.
Otherwise head north or south on the gateway and see if you can find something.
They're not mountain roads, but the tourist roads in brighton/redcliffe etc are nice and curvy. Few parked cars though.
Maybe just head northwest towards Strathpine/Cashmere, head in the back way to Samford, and then tackle one of the mountains.
Head home through Gap Creek Road if you feel like taking the tractor on the cattle run.