I play a bunch of
and consider her my main. I play her Top, Bottom, and Mid. Often times i see a lot of people use a build similar to yours. Personally, I think it's trash.
My reasoning as to why it's bad is that it has so much attack speed. Quinn's huge weakness is that she has a shorter range, so this means fewer times to deal damage in team fights. Huge AS steroids just don't get used on her imo due to the danger involved.
Regardless of where i play her, this is my standard Start on Quinn.
(Boots flexible, whatever you need)
Now I choose this build path because it feels like the strongest start on her for me, and maximizes the typically 1-2 Trinity Force proc's you'll get in a single skirmish.
You should really play Quinn mostly as an assassin, as her kit is INSANE in 1v1 fights, especially in Valor form. With just IE and Trinity you can R>E>Q>Auto>R and kill a carry if they have no armor or health item yet. If you somehow don't kill them, they have like, 10 hp and you just shoot them, all before your blind wears off on them.
As such, my Quinn builds usually look like this.
For Max dmg against non armor targets. (for armored substitute LW for youmoos if they have like, 3 armor items. You shouldn't really fight them if they do anyways, kill something else)

For more tank
(finish hexdrinker after randuins)

I really don't stray from those 2 builds, but you have to be mindful that you won't crit much with the tankier build and as such assassinations have a bit of an RNG to them.
Overall my opinion is "Yes" to trinity force on Quinn, but don't build attack speed to back it up, build raw damage. Those 2 sheen procs need to HURT to make it worth it and BOTRK/TF/Youmoos just doesn't hurt at all.