QF was one of the few Legacy airlines (with new Boeing 747's on order) to be a solely 747 operator for quite a while...
I can also think of Virgin Atlantic who from 1984-1993 were a 747 Classic only airline with 8 on strength by 1991
Wardair I think flew only new 747's for a bit, until their DC-10's arrived
Was there any one else (Legacy or main stream airlines) who only flew 747's?