Hi HoboMcJoe, thanks for commenting! I had a hard time placing Fizz on a scale of 1-10 simply because the skill of Fizz players can vary so much. It's true that skilled players may pose a huge threat to Anivia, even early in lane. However, there are things you can do even if the Fizz is better than or ahead of you; for instance, farming only with your ult. I try to think of all the different strategies an opponent can use, but I'm obviously going to miss some, so thank you for giving specific feedback on something I missed!

In response to your specific question, don't panic if Fizz uses his Q to get close to you. Just walk away - after all, he just used his gap closer. If he retreats, you're fine. If he uses his E to reach you, you can stun him right afterwards and easily win the trade. That's the key: always save Q until after he uses E, even if he's uncomfortably close. I'll update Fizz's section ASAP and reconsider his threat rating, but here are three things to remember when fighting the Fish:

1. Not using your Q will force Fizz to not use his E unless you're really low on health.
2. Fizz is even more mana-hungry than you early in the game, especially if he has to spam his E.
3. He's melee, so he can't usually kill you in egg form if you're under your tower (don't be afraid to flash there even if you're about to die).
(4. Birds eat fish)

Check out my updated Fizz section (should be done really soon) and if you have any other questions, or if I didn't answer yours correctly, please comment! You'll be helping everyone who was wondering the same thing :)

P.S. Recently someone stole my Anivia, forcing me to pick Fizz against her - so now I have experience from both sides. (I won) :p

TL;DR: I'll update my Fizz section very soon. If he uses Q to get close, just walk away or stun him after he uses E, never before.

Can't agree with placing the fizz matchup as a 2. I know you said that it is not because you are just facing bad fizz players, but that is what it seems like because a good fizz will just use his q to get close to you and the second he sees the cast animation for your q he will dodge it with his e, then you have no cooldowns to fight him. You have to give a good fizz a ton of respect and try to freeze the wave or you lose lane.