Quinn is a bit of an oddball champion. She's not really a Marksman, not really an Assassin, and not really a Diver, but can kind of fulfill all three roles to moderate success.
I have to disagree with you that her laning phase is poor though. In fact, I'd say she's a very competent laner, and can go toe-to-toe with an astonishing amount of melee top laners, mid lane mages, and assassins. However, her kit is so superbly strong against melees (in large part due to Vault) that I presume buffing her would make her far too oppressive up in the top lane.
I do think things get hairy for Quinn once enemies start stacking armor though, particularly top lane supertanks such as Galio or Maokai who, upon purchasing Ninja Tabis, can freely ignore the brunt of Quinn's harass. This feels terrible for the Quinn player, but is also balanced by the fact that she has the power to just shove in and quickly roam for picks on squishier foes.
Honestly, if it were up to me, I'd shave away some of Quinn's anti-melee and Marksman-like properties in favor of just making her a pure mid lane/jungle Assassin. This would probably entail reworking Vault into a linear skillshot rather than a targeted effect, and removing the AS steroids from her W (along with some of her AA range) in order to give her an escape mechanism that allows her to escape fights after entering them. I'm not a game designer, so I don't know whether those tradeoffs would be appropriate -- but overall, I'd prefer if Riot just solidified Quinn's identity as an Assassin and gave her the tools to support that rather than leaving her as a champion that is mediocre at everything except moving around the map quickly.
