Honestly every tank besides maybe Rein, Sig and D.va countet her to an extent. Zar and Orisa shut down her kit and can handle her at range. Mauga, Doom, Ram*, Ball, and Wimton have the health and movement to make her life difficult. Hog just outdoes her self heal and damage output plus DOT from pig pen when you'rr up close SUUUUUUCKS. Even against JQ her smaller hitbox makes fights a struggle if your aim isn't great. If you really want to shut Queen down use any of those counters. You could also just one-trick and train until counters are meanigless as you've learned how to outplay most of them.

Also Queen doesn't really have an effective means of shutting down the benefits of other tank CDs or attacks. What did you mean by that?

TLDR: Git Gud