Does BA still go to Australia?
The only BA operated flight is to Sydney, hence it's notoriously difficult to get reward availability. But you can get to HKG or SIN or KUL (or even China or Japan) and fly on from there with stopovers to de-risk the separate ticket connections.
PS please don't "hold a koala". It is very stressful for the animal and is banned by most states. Feeding is ok.