How To Play Quinn?

So I have played Quinn for a few games and I must admit she's fun. Her roaming capability is just amazing. Unfortunately, I feel as if I haven't fully understood her role in-depth especially in team fights. She's a Marksman, yet her dashing skill puts her closer towards enemy instead of further. I play her like a burst champion. Before a teamfight, I would get into Valor mode so that I can make use of that ultimate's damage, which puts me in the middle of the fight, I would then Q, basic attack, E, basic attack. You get the drift. Basically I make use of the Vulnerable trigger that comes from those spells. Most of the time I feel the need to close the gap between the enemies and myself to achieve the most damage output in the shortest time, which eventually get me killed, even with my teammates around. The reason why I feel the need to put myself at the risk of dying is because I feel that she doesn't do a lot of damage with just her basic attack like Caitlyn or Jinx would.

How do you play her?