Change the character’s face without starting over

You are not stuck with your initial decision!

Luna lets you know that you can update your Dream once a day (and only once a day) to update the version of your town that everyone else sees. After speaking with her today and confirming with her that I wanted to update my Dream, she asked me again about whether or not I wanted to make my patterns/designs publicly available.

So there's no need to delete and remake your Dream if you're worried about this, as every time you update it, you'll be able to choose your preferred setting.

No, you can't change your face or gender after creating your character, you'd have to make a new one. You can however make a new, non-mayor character that is female (they will have to more or less start over with various things like house payments, encyclopedia, catalog).

In addition you can also use a Mii Mask from Harriet to look female (I believe you can use a different gender's Mii mask anyway, I haven't tried). And if you wear a female "dress" type item, your character's animations will actually change to the female animation set (note certain "dresses" are unisex or male clothing; as a male Able will make a comment if you attempt to buy female clothing, those dresses will change your animations). I'm not sure if there is a way for female characters to change to the male animations.