|Her helmet looks pretty gay.|
Quinn hasn't been out for long but it seems she's not a typical attack damage carry. In fact, all the research I've done indicates she would perform better at top or mid as a counterpick. Her short range makes it hard for her to beat a fair few carries at bottom lane. Don't get me wrong, if you know how to play her you can succeed anywhere on Quinn, she's not a bad champion. She's the second character on LoL to have a blind, following in the footsteps of Teemo.
There are already several ways to play Quinn, she works well as an AD caster mid, or a bruiser top. With the incredible speeds she can achieve with her ultimate she can gank other lanes with ease. I've personally been taking her top most games, because she can deal with almost every common top laner without too much trouble. She can bring a fair amount of utilitiy to mid and late game team fights, however she's very squishy and her ultimate is on a very long cooldown.
Regardless, Quinn is a fantastic champion. Expect to see her incorporated into the meta in the next few months. Try her in different lanes, see which one you prefer. Also, if you have any additional information on how to play her- let us know with a comment!