You can access any oneworld lounge (not third party lounges) under class of service rules.
You won't be able to access CX as its in Terminal 4.

But you can access the Qantas and BA lounges in Terminal 1 (they are next to each other)
If your flight departs from the B gates in T3 its fairly close, if its A gates its a bit further.

Note however that both lounges have limited hours
Qantas - 14:30 to 23:00 Daily
BA - Daily: 15:00 - 23:00
So you'd be out of luck for 2 of the 3 SIN-DOH flights