I would say buy some Avios from BA via their subscription or one of their sales but pretty sure since you're on AA codes you can't upgrade it with miles at all. There are some exceptions out there, but usually to use miles for upgrades it has to be the airline's own miles, their code, and their metal. Avios in this case are the common currency of QR, BA, IB, EI, and one of their LCCs, so you can interchange them from BA to QR without issue if you buy them from BA.