Just a non-art related quickie.
You say you want it to be quick, so that the player will have to react quickly before it comes too close, right? And that the attack animation has to be fast, so the player doesn't have time do avoid it, right?
It's easy to balance that out. If you want a fast, hard-to-dodge enemy, a zombie is obviously not the way to go. You want another enemy for that. If you really do need zombies, though, you shouldn't have them fast and swift like that. Balance it out in gameplay. Slow them down a lot, but make them be able to take TONS of damage. Make sure the player can't run (surround him in zombies, in other words!) and just unleash slow, rotting death on him. It'll be the same thing, but in slow motion. Meaning, if the player is too slow to react, the zombie just won't die until it's too close, despite taking constant damage. Same with the hitting animation. If there's a zombie on each side of the player and he can't just run through them (I hope he can't, being trapped is a big part of zombie games), it doesn't matter how slow they are. Just make them do more damage in turn.
Oh, hey, a demo! I didn't notice that. How silly of me...
Mmmyes, I definitely like this. I love these kinda games. They REQUIRE fast enemies, though. The zombies feel slightly too fast, and slightly too weak. Try to save the regular kind of zombie for enclosed spaces, and have TONS of them there. Also make sure the player is rewarded for his kills, because it's always far too easy just to run past enemies in so many games. Including ones I've made, myself. I always come back after a while, sigh at myself, and think "Why couldn't I have made this harder somehow?"