I think the problem with QR is the lack of widebodies for BHX. They dont have the constant deliveries of aircraft that EK has, so expansion is slower for them.
There is a very slight rumour MAN will be upgraded to a B773 (to keep up with EY/EK) which would release an A333 (likely to be put on CPH or somewhere, in turn, their A332 could start BHX). The question is, would QR come or have they got bigger fish to fry?
I think if they at least started 4 weekly at the same time as launching another service 3 weekly (to fill the gaps), QR could do well at BHX.
It will be a long time until EY comes to BHX though, as they have retreated to just the LHR/MAN core routes, and Ill tell you now, EY will be out of DUB faster than you can say boo if EK enter the DUB market as they only seem fight in the big cities .(MAN seems to be a strange exception as one of only a few Euro cities to support all 3)