Based on what you mentioned, I had no idea. It didn't make sense.
But - I found a bit of the script online, and it mentioned that they were playing cards at the time. You didn't mention that, and that made all the difference!
A queen is a card - and in many games it is a reasonably valuable one.
(edit) I just read Zach's comment. My interpretation is slightly different - I think she was pretending to want to cheat, by asking the dogs if they had any cards hidden, that they could give her.