And with the ongoing shortage of frames at BA due to the 787 engine issues, I think many on the BA forum would wager that BA will continue to cancel the LHR DOH flights this autumn and transfer those passengers onto QR.

If you can get native QR flights you would be guaranteed access to the QR lounge at LHR T4. However I suspect that you might not be able to pick a flight that is scheduled to be Qsuites flight as there is usually a price premium on these flights (I've not checked the detail in this case). Whereas rolling the dice with a BA flight on the presumption that it will get cancelled onto QR you have a good chance to argue the case to be rescheduled onto a Qsuites plane.

Note that trying to book QR to be on a specific type of aircraft and seating arrangement can be akin to gambling. Number one rule on the QR forummon FT - dont book a QR flight to be on a specific type of aircraft. Some routes are better than others for having a stable aircraft assignment. Looking at seat maps on qrcargo.com is a good source of info, there is more certainty from 2 months out, but until you arrive at the gate you really can't be 100% certain your plane hasn't been subbed.