I do this route often, using using BA Avios but occasionally using my QF points (just to keep my QF account active). Availability on the QF website can be tricky. Those flights are rarely full (except very peak times at peak times of year) and BA typically release additional seats on that route (in both cabins) into reward inventory at a few minutes after midnight, the day before travel. However, for early flights (i.e. around 32 hours later) that's too late for a QF FF reward ticket to be issued because in QF time, it's already > 24 hours before travel. If BA economy is currently available ex LHR, my advice is take it. There's little point in an upgrade on that 50 minute flight and trailing from LHR out to LCY just for a J seat would be grim. If you're desperate for an upgrade, ask at BA check-in at LHR: it may be available for around £69-£89 (which, in my humble opinion, is not money well spent for a 55 minute flight).

And if you're absolutely struck, remember you can fly LHR/DUB on BA and then get a frequent coach (every hour or so) from Dublin airport to Belfast. The coach takes around 1.5 hours and costs around Euro 15 (or half that if booked in advance). That hassle and cost of the coach is broadly equivalent to the hassle and cost of traipsing from LHR out to LCY i.e. both are do-able but avoid if possible.