Looking at a redemption on Qatar from HKG to LHR but nothing available when I want it.

There is however direct availabilty to DOH (Doha) and also onwards to DXB (Dubai)

One QR flight into DOH arrives at 22:30.
There's a CX flight arriving into DXB at 6:45am if need be.

There is a BA flight from DOH to LHR at 11:45pm or somewhere around there but that's probably pushing things if connecting from the QR flight!

DXB is more favourable with early and late flights.

Is there anything to do at 10:30pm in DOH or is it a case of getting a hotel for the night? (options connecting to another QR flight to DXB range from 1-9 hrs)

Redemption searches:
If I select HKG-DOH, I get offered nothing on the day I want. Go to the following day and 1 flight in business.
If I select HKG-DXB, I get offered 2 x CX flights direct and 5 x QR F from HKG-DOH and then QR F DOH-DXB.
Why can't I get offered the same flights for just the HKG-DOH search?

If I then go to the payment page, the HKG-DOH flight comes up nicely as 40k + £77.
The HKG-DOH + DOH-DXB flights won't work online
(separately, yes, with the DOH-DXB flight in F coming in at 13500 Avios + £64.90 tax which seems rather steep for a 1h10 flight!) - any way of knowing the total tax without ringing BA?

Also, regardless of what the BA availabilty calendar says, there seems to be BA availabilty every day. Is there no way or seeing any other airline?
Would rather fly QR.