I would guess BA would offer / you could ask for a reroute via DOH, e.g. BA 123 (BA prime) or BA 7008 (operated by QR), then BA 6346 (operated by QR). You'll need cabin availability, but not necessarily Avios availability AIUI. Unfortunately QR has no WTP, which means your wife will end up in economy. I'm not knowledgeable about QR but it may be that QR economy is better than BA WTP.

There's also a Quantas route that changes in SIN but I don't immediately see BA codeshares on it.