Why can't I change my eye color in New Leaf?

You should be able to change your eye color after the following conditions are met:

1. Shampoodle has upgraded their equipment.
2. You have changed your hairstyle and waited 2 weeks. (This might be the one you're missing)
3. You must be in your own town
4. The gates to your town must be closed.

Additionally, the color of the contacts you receive will depend on how you answer Harriet's questions.

Hope this helps. Let me know if I've missed something or if this doesn't work for you.

EDIT:

I believe that since your character is new, you probably have to wait the 2 weeks after changing your new character's hairstyle before you can get the contacts.