I recently linked my BA and QR accounts and I haven't yet transferred any points. Both my accounts show the same number of Avios though-- these are points I recently transferred to my BA account from Amex (40% bonus!).
Now, when I search for award availability on QR, while it doesn't show me the "you don't have enough points" message, I can never manage to see any availability at all. Even if I see the same QR flights available on AS and BA, the message on the QR site is "There are currently no flights matching your search. Please try different travel dates or itinerary."
I booked a QR Business award on AS but couldn't even see that same flight available for award redemption on QR's own website.