Annie is a very versatile champion and is certainly viable mid.
In fact, Annie has the advantage against Zed. She is one of the few champions who has access to a frequent stun in addition to it being unavoidable.
Try to stun him as much as you can before 6, and build Zhonya's as a first or second item. Always clear his minion wave ASAP so you don't take aggro when you AA him, and to prevent him from shoving his wave to your turret.
A good stun after level 6 will completely counter Death Mark. During mid game and late game, you will be able to kill him with R, W, Q alone. There will literally be nothing he can do to you as he would not be able to kill you without his ult, but if he does ult you can counter ult, stun him, and blow him up.
This aspect of her also applies to every other melee assassin. She wrecks champions such as Yasuo and Talon with ease, Zed is only somewhat challenging because he can retaliate a bit with his range.
The primary reason she isn't a top pick despite her dominance over melee champions is that most other mages out range her. Champions such as Kat has to walk into your spell range to do damage, in which case you can immediately stun them. However, long range casters such as Ziggs or Viktor can stay from afar, forcing you to walk into their range first before being able to stun them.