Getting stuck there is not a problem for non-residents, there's plenty of seats out, unless there's issues at the final destination after leaving Australia. The problem is being flexible enough to reach Australia in the first place!

At the moment BA inventory is not anticipating the limits on arrivals continuing, but I would not rely on BA to get you there, comparing to other carriers which are closer to the market. I noticed there is availability on SYD-SIN on BA from the 16th Dec onwards. BA is offering, for example on the 16th Dec: F5 A0 J2 C0 D0 R0 I0 W9 E9 T9 Y9 B9 H9 K9 M9 L9 V9 S9 N9 Q9 O9 G9. By contrast SQ have reduced their flights to single daily (with a second some days continuing to BNE) and on same day (16th) is offering: Z8 C0 J0 U0 D0 Y0 B0 E0 M0 H0 W0 Q0 N0 V0 G0 K0. And QR DOH-SYD is just J0 Y0. I suspect the latter two are more likely to be an accurate.