I don't hate the hand. I think villain is more likely to fold if the board was QQ77x than QQ99x, and he just convinces himself that you bricked your JT or something.

That being said, I'd prefer to run lines/plays vs villains when their range is capped and I'm confident in that. In this spot it's not unreasonable that he plays Qx this way, so you're going to be bluffing into the nuts somewhat often.