Why do you have miles with AA and BA and QR? Did you fly QR before they joined oneworld in Oct 2013?

QR is the only one of those 3 that has such strict expiration policies, so if you already have an AA and BA account, it would make sense to credit all QR flights to either AA or BA (from Oct 2013 onward).

No, it's not possible to transfer miles between the airlines after the fact. That's why you want to be really careful about choosing which airline to credit for any particular flight (and to know expiration policies before you join a frequent flyer program).