There is a soft code share where QF only pay for the seats they use whereas before Big red would pay for a seat allocation whether the seats where sold or not. I believe that the same applies for PX selling seats on the QF 737. Effectively Big Red would prefer to sell seats on its own Aircraft thus competing directly with PX. The reason the code share was kept in any form was because of the limited J class capacity of the QF 737 and a desire for the ability to ensure seat availability for their J class customers and keeping VA from poaching any. I think it would be very unusual to see QF Y class customers on PX aircraft with the exception of peak periods.