In your defense, Quinn does have a blind spell and Fiora relies on auto attacks as an AD melee. If that's why you thought you stood a chance, then it's actually justified and good reasoning, it's more thought than I see some players put behind a matchup. Personally though, I have a priority list of comparing my champion to my lane champion that tells me whether or not I think I have the advantage or the disadvantage.
- Summoner Level/Runes/Masteries/validity of build
- Champion Role
- Champion strengths/weaknesses relative to abilities
- Rank level
A higher number ignores any of of its lower numbers, and two lower numbers ignore the one just above the higher of the two lower numbers:
Since Fiora is an assassin, assassins dominate squishies, and ADCs like Quinn are squishy that dominate tanks, I would have immediately felt Fiora had the advantage in a 1v1 even if your blind potentially reduces her overall damage. Even if someone is willing to argue about Quinn's potential in this match up, to me an assassin is a hard counter to a squishy, period. You chose scissors, they chose rock, in my personal opinion it's that simple. It isn't to say Fiora will 100% beat Quinn, but a Fiora clearly has the advantage if knowledge/skill levels are even. If you're not carrying 90% of the games you're in as a top Quinn, then when you saw you were going against Fiora, you should have heavily insisted in champ select that it would benefit the team that you adc or jungle (assuming you were in a draft pick), and if somehow unpreventable in champ select (like you being in blind pick), then heavily insisted a lane or jungle switch with you. You and your jungle being behind because they have smite as top and you don't have smite as jungle is a more mitigatable circumstance than a fed Fiora.
So lets just assume that in the future you decide to take another Quinn as top, you get get paired with Fiora, and your lanes refuse to swap with you:
Knowing that I am only an average player and knowing what I said in the first paragraph, I know I would do absolutely terrible against someone that has the role advantage like that. I don't even pretend that maybe they're bad enough for me to handle them and just do my best with my fingers crossed (figuratively); I would take every necessary step to prevent feeding kills to Fiora even if it forced me to be behind. I would rather me be behind, never having fed Fiora a kill, than hoping our circumstance turns around the moment I'm able to catch up in mid or late game.
I would have taken my typical runes and masteries (maybe would have considered taking my AD melee runes because they have +12 armor instead of the typical +9), taken teleport (assuming draft pick) to help me retain a presence in lane so I don't get behind in XP and potential last hits, started with and max my Q first, rushing Zhonya's even before first tier boots (to make her ult irrelevant) before straight AD items (her Q scales off of both AD and AP, though more off of AD), and would have done my absolute best to survive by poking her down with at least Q (I'd try to do as many passive mark+aa+e+aa combos as well), and if she was too stupid to back. bursting her down with that combo, my ult and that combo, or flash and that combo.
I am not saying this is the best strategy. Like I said, I am an average player. I assume if you played Quinn often enough to know her capabilities, you doing something different than my suggestion wouldn't even be argued against by me, but if I am ever forced to lane against a champion who has the role advantage, I typically am not risking feeding unless I notice they aren't playing/building the champion properly and are making lots of mistakes. Or like, in normals, when LoL Nexus tells you you're playing against a level 23 because of party queue, their rune/mastery pages aren't going to be complete and are generally going to make them super easy to zone regardless of their role advantage.
+ 
+ gromp buff + w = fiora took more damage from her ult than you did from hers
either that or just cc lock her