Am I quinning wrong?

So I LOVE playing Quinn. She is the only champ that I have picked up and played for 60 games straight without getting bored with her. The only problem is...I suck.

Well I don't actually suck, I have a decent win rate in line with other champs I consider myself to be good at. But my damage is really low in comparison to other champs I play and normally the other champs in my game. I love the utility she brings with the displacement and her W, and I normally run TP and just harass objectives all over the map, and I win lots of games by splitpushing but her mobility (and TP) allows me to get to most teamfights when im needed.

Don't get me wrong, I lane pretty well usually, and tend the hold my own or punish champs for cs etc if I am behind, and sometimes I get fed, but I struggle to see that power in mid to later game, and the damage dealt at the end of the game is often disappointing.

So I guess my question is: is this part of the champ? Does her utility triumph over what I see as a low damage output, or am I doing something wrong?