How it works in reality I cant say but how it works in theory accd to the rules is that you can have a stopover if it's the most direct route to your destination. Lets assume that Perth is your destination then Cairnes and Sydney are not the most direct route. Singapore is so if you stop there then your route would be. In practice, I dont think you would have many problems going through Sydney, but accd to the rules it should not be allowed. It used to be that BA's partner awards allowed you to use BA *and* the partner. The text has changed on the site so I dont know if this is still the case. If it hasnt then maybe you could use BA to Sydney (since they no doubt would rather have you on a BA plane than a QF plane since then they dont have to pay much to QF for you to go) and then QF to Perth. I expect if they allow the routing then they will allow the stopovers. Im sure you coulds probably find a decent priced ticket to Cairnes from either Perth or Sydney.

Another option is that you could probably do close to your proposed routing with a Oneworld Award for 20k extra miles. Great Circle is down so I dont know exactly the mileage but I think you could get it under 25k with a bit of ingenuity and planning.