Personally, I would book for about a 2:30 connection. There's no guarantee that you'd make it, but most of my personal international -> domestic connections have been OK at between about 60 and 90 minutes, and this would give you an hour extra for margin. (You might have been able to take a more laid-back view about a misconnect if it had been a QF -> QF connection, as the likely reason for a misconnect would be QF's inbound delay, but that's not your situation.)

As I'm sure you've realised, you'll have to collect your baggage at SYD and clear customs with it. You can't through-check because of the customs clearance required.

I'm not sure why you can't use the QF bus transfer from the transfer facility in the international terminal, arrivals level. You are connecting onto a QF domestic flight, after all. That's worth a try. It takes a lot of the hassle out of it because you check-in there and hand over your bag, then get on the bus. When you get off the bus at the domestic terminal (T3), you'll go straight up to the gates.