re-raise for sure. If you're not going to with QQ, what is your range to do so?
I don't know about folding at the end either. You have to call 4.43 with 5.60 already in the pot, so the pot odds
are better than 2:1, which means you profit if you win one time in three. You'd be better placed to gauge if your overpair is enough to do so if you had re-raised pre-.
And why show? To prove to him that he can push you around? He's more likely to think that than to respect you for being able to read him and make a laydown, especially if he doesn't have you beat, like with JJ. And even if he does suddenly respect you, how are you going to take advantage of it?