No. I purchased the ticket on the Qantas site so it was on their own ticket stock. But now that I go back and read the post again I see I misunderstood and that it says Qantas is one that is included. My apologies.

Only once did I fly Qantas a few years back on AC ticket stock and that was because AC bumped me from a flight and messed up my trip. I would not leave the counter until they fixed it and that meant they had to issue a ticket for me on Qantas and it was on their ticket stock.