That makes sense, not being able to check the bag through the same airport twice!
Is it worth asking at Heathrow if they can just check the bag LHR-DOH-Asia? I'm guessing not. And the length of time (almost 27 hours) might pose a further issue.
I think I'm going to go with the booking regardless - a 2h5m connection at DOH should be fine, and if not I'll try to move the first leg of the SJH-DOH-Asia booking to a later time.
Thanks all.