I play her a lot in Dominion, I'd say Sauron placed her pretty well in his tier list on that matter. She's horrible at clearing minion waves so you don't want to play her bottom lane. She's pretty strong at level 3 (a double lunge and burst of speed combo can bring most champions below 50% health), then needs to get something big to start dealing damage (I like Youmuu's, as she has major cooldown issues and she can put the active to better use than most).
Her kit makes her more viable than Yi and Tryndamere, mainly because her ultimate is way better. For all intents and purposes she's pretty much invulnerable and immune to CC with it, while the other 2 just get one or the other.
That said she isn't particularly hard to counter and her all-in fighting style isn't the greatest on a squishy champion, so against competent teams you'll want allies that can initiate for you to take the enemy CC and exhausts.
Exhaust generally means she dies, which is further compounded by the fact it reduces her ultimate's damage by 70% (considering it's on-hit). When she gets blinded or Exhausted the only move she has to reliably target champions is lunge, which is a little depressing because the mobility is generally better than the damage. Being so susceptible to a summoner spell alone generally means you should really pick up Cleanse on her, otherwise you stand pretty much 0 chance against anyone that can kill you in the time frame exhaust is active.
For counters Jax is pretty hard for her to deal with, mostly for the same reason Blind and Exhaust are hard to put up with - she is so auto/on-hit reliant his evasion prevents damage from everything but lunge (and riposte, to an extent). Teemo can be annoying, but he only counters her if you have bad positioning and are overly effected by the global Teemo taunt.
Ezreal is perhaps the most annoying champion to face off against as Fiora, as his slow, flash, and long-range poke that applies Phange will allow him to kite you endlessly. He's better in the Jungle than Fiora because he can kill things he can't see, he's better in the open because he can kite endlessly and easily escape, he's better in poke wars because he has poke. And it wouldn't be so annoying if he was also the best ADC in Summoner's Rift already.
In the end, Fiora is certainly playable in Dominion, and overall pretty balanced. You'll just feel at a disadvantage if you're fighting against the overpowered crowd.