There was no preflop raise, It is highly unlikey you're up against a better queen. I would put him on a worse queen and jam that pot to the river. If he has a worse queen then yes your WA but guess what? he's not folding.
The entire point of the concept is don't make only the hands you can beat fold. There are tons of hands you can beat that are going to the river with you no matter how much raising you do. It does not apply here.