That's the biggest downside to qot is that in a 3v3, unless there is a reg on your team, etc, qot quickly becomes the primary target in most circumstances as she generally has lowest hp. And she can only run so fast. You don't see many games where qot ends up with jtreads. Then take into account a batswarm+lv 2-4 stun (which she obviously can't get away from, followed by X, followed by Silence, etc. That's not to say that she can't be played incredibly well. No arguments at all that she can deal out quite a bit of punishment - and on a good team, that extra dmg + slow is huge.
Not quite sure what sort of QoT build you are using anyway. At any rate, keep playing her and beat up folks that underrate her as possible.