Hi!
A couple of things...
First off, know that brushing her teeth before bed is a great idea to get your child in the habit of good oral hygiene while she's young so it's ingrained, but it's not a protective effort particularly because all of those teeth are going to fall out at some point or another. So don't worry about that :)
But I can totally relate to the sleep thing - I'm going through much the same thing with my 17 month old. I have two suggestions that other people have told me worked for them...
1) Yes, there are ways to "dry out". I know there is a really good tea made by earth mama angel baby (don't have the website handy) that is supposed to suppress milk production. You can also try wearing super-tight bras and keeping cabbage leafs over your breasts (I know, weird but time-tested!).
2) I don't know if the baby's father is with you or if you have a partner, and even if not, maybe you can have a *super close* friend or relative whom your baby is comfortable help you with this one... but for a few nights until she gets used to it, have someone else who your baby is close with take her to bed and tend to her at night. She won't like it, and will cry, but if she is with someone who loves her and will help her feel secure, and she will sooner or later give up, knowing that "mom's all-night cafe" is closed.
I hope that's helpful :)