​​​​If this is QR DOH-AMS, and then BA AMS-LHR-SNN then you should be able to check baggage through under QR's current policy. (You seem to omit the AMS-LHR sector above). Worth checking with BA at the earliest opportunity in AMS that your QR bag tags have been captured in their check-in systems and loaded correctly on the aircraft at AMS.

Note that QR will check your baggage entitlement on BA and if that is less then the QR J entitlement based on what I have seen they will only check in what your BA ticket will allow.

Can't comment on experience at DOH but I would expect less problems there than elsewhere as more people are likely to be trained on current policy. It's outstations that usually experience variable outcomes.