nah, already checked. none of the cheese variants are even appearing in the list of options when she asks.
1. Use the fairy dust in the Fairy Grove. 2. Give the Queen any milk or weird fish. 3. Go to the Queen and talk to her. 4. The Queen will offer to play a game - play (the result of the game does not matter). 5. Talk to the Queen again and choose the question about the giant plant. 6. The Queen will ask for another gift - and in this case you can choose cheese.