Q: 4 (2 if she kills a minion with it)
E: 14 / 13 / 12 / 11 / 10
R: 120 / 100 / 80
Annie's Skill Max Order: W → Q → E
Level 1: Conduct Quinn Cheese. Annie will retaliate with her Q. You hard win the trade, so just run her down with autos until shes under tower. Now, you can either stand between minion wave and her to zone her off, or walk back so that she walks up away from tower, which puts her at a vulnerable spot for your level 2 all in.
Level 2: Annie should be half health or less. Pay attention to her stun bar because that's her only threat to you. You hard win all trades, just be careful if her stun comes up.
Level 3: Annie has her E now, which is kinda tricky. If Annie has 2 stun stacks, she can stun you by using W-E quick before her Q to get a stun on you, but she can't follow up after that. Her E makes you hurt yourself when you auto her, so pay attention to when she uses it. It lasts 3 seconds, so if she ever uses it, you have a 14 second window to play aggressive because it's her main form of defence. I would try to freeze wave against Annie so she can't get her Q stacks on the minions, which makes her useless since she can't stun you as easily.
Level 6: This is where the lane becomes unfun. You must be extremely careful about your HP because she can 1 shot you if you're too low. Her R range is the same range as your E, so stay back that much distance if you can if you anticipate that she wants to all-in you. I would look for roams post 6 if possible, but if you have to remain in lane, stay far away from her and go for trades when she uses her stun on a minion because she won't be able to ramp up her R stun in time to use it on you.
Play around Annie's stun passive. Level 1 she only gets 1 per ability, so play level 1 super aggro. When she levels up more, her ability to punish you increases. You want to ideally kill Annie pre 6 so her R isnt as scary.
Early game she can't one shot you, but her stun makes it hard to all-in her. Take trades when Electrocute is up, and remember that she has no sustain, so one good short trade is incredible for you.
Her W range is the same as your E, but her Q range is longer.
Stay close to Annie so if she throws abilities on you, you can retaliate with ease.
Try to freeze against Annie so she over extends to an unsafe position.
If you want to engage on her, E her first, and she will eventually get her stun off. That is okay thought because if you E first, she is slowed and you can still run her down after the stun wears off so long as you land E first. If Annie ever uses stun, punish her instantly hard, especially if she uses it on minions. If you freeze, Annie will lose CS because she will not be able to last hit that well if she holds on her stun. She is forced to use Q on a minion eventually, but if she does then she is dead. If she doesn't, then she will lose CS. Freezing is op in this matchup.