You most likely know a lot on how to play against Quinn, I’m just showing you some examples of counterplay and some general tips for other people that might need it.
Well if you have any ranged poke then you can deal with Quinn very easily. Quinn is only good in melee matchups, and even more against full melee champs (like Garen and Mordekaiser), she struggles hard against ranged champs because she can’t easily get her combo off without receiving some or a lot of damage, she is really squishy so any poke is really effective against her. And if she is pushed up she is very easy to gank if your laner (if you are the jungler that is trying to gank Quinn) has Quinn use e and hopefully q too right before you gank. That way she is forced to use flash to escape, which opens her up for a free kill if she pushes up again and your laner does the same thing.
Using CC on her after her E and making sure you are behind minions when she goes for a combo will help a lot in trades. Your minions will block her q if she tries to use it after getting the first harrier proc from e.
Oh and BACK THE FUCK UP WHEN HER PASSIVE MARKS YOU. Not the part where it marks a target hit by q/e/second part of R, but the part where Valor periodically marks a nearby target. This situation gives her a lot of damage in a trade and depending on your health, the quinn’s Items and runes this situation of her combo (first harrier proc, e, another harrier, electrocute proc, q, another harrier proc) might be enough to kill you without getting return damage/kill on her.
As a Quinn player (kinda main) I have experienced all of this, as both the Quinn and the melee champ she is dicking on.