you are entitled to your beliefs about fairies and magic...
I dont see the harm in the whole tooth fairy thing, though. It's a fun childhood thing. Are your children visited my Santa Claus? What about the Easter Bunny? I'm just curious... I'm not judging, that is not my place. I guess I'm just trying to understand the reasons behind your choice with the tooth fairy or even letting them watch cartoons with witches and fairies.
Then again, I'm a Witch, not a Christian, so my view on those things is quite a bit different and I am far more open minded than most Christians that I have come in contact with (and I am a former Christian as well, I grew up in the Mormon church and attended Catholic services as well).
As far as ideas that don't use magic or fairies...
Maybe make a big deal out of losing the tooth in an unrelated way. I bought a little ribbon that was an award for losing the first tooth for my son. I got it at Dollar General and he was so excited to get an award, he even momentarily forget that his mouth was bleeding. Maybe let her have a special treat after she loses the tooth - like a bowlful of her favorite ice cream and toppings, pudding, or jello.... just avoid crunchy toppings because her gums might be a little sore.
If you don't like using food as a treat, maybe you could make a keepsake together out of the tooth. It could be picking out a box (like a small wooden one) to decorate together to keep all of the teeth she loses in until she's lost them all, then you can decide what to do with the box at that point. She could bury the tooth as a way to say goodbye to it.
If you're not completely against magic and fairies, you could still do the whole tooth fairy thing - then encourage your daughter to give whatever money she gets to your church (tithing or collection plate, or however else your church accepts donations). That way she's getting a bit of the fun (and wont feel left out if other kids talk ab out the tooth fairy) but still learning an important lesson (about giving to others and being generous).
When my son lost his first tooth, I used it as a way to reinforce how important it was to take care of his teeth - because now he had a grown up tooth that he would have forever. (He already brushed and flossed his teeth, but it was a way to talk about being a big boy and continuing the good habits.)
If she doesnt use mouthwash already, you could introduce her to one of the children's mouthwashes (like ACT) after she looses the tooth - as a sort of rite of passage (cant use mouthwash til you have at least one grown up tooth or something like that).