You could tell her the Tooth Fairy also comes and checks to see if children have brushed their teeth. The Tooth Fairy could come AT ANY TIME and if she brushed her teeth she will leave a sticker. If she didn't brush her teeth she won't leave a sticker.
Then buy a package of stickers. If your daughter brushes her teeth, leave a sticker (with the backing still on) where she leaves her toothbrush for her to find the next day. We used very tiny cheap stickers (once I used smiley face stickers I had gotten free in the mail!)
You can reward her every time she brushes her teeth, or you can make it so the Tooth Fairy only comes sometimes because she's so busy. Stickers are cheap, so it's not a heavy cost!
Most kids love stickers, and they love the idea of the Tooth Fairy checking and leaving a sticker. We use the House Fairy now to keep her room clean. The House Fairy could visit at any time and leave a surprise. You wouldn't believe how good that works!