They will only check you to SJH on your first ticket. 2h in DOH transit is plenty of time.
There can be all kinds of IRROPS when flying but that is a minor one.

Assuming that your LHR flight is heavily delayed, then you can argue when you arrive in DOH.that because of felay you don't need you SJH business meeting anymore because of QR fault and wish to be routed directly to Asia from DOH. That might or not work.