Personally, I love teaching young kids, and I am a strong proponent of such, for the right kids. They need to be comfortable in the water, have the right maturity and attitude, and have to want to do it for themselves, not for someone else. Given that, I think its great to get them in the water. With all the difficulties they face growing up, peep pressure, drugs, sex, violence, etc., to me, having a healthy hobby like diving is a big positive in their life. I have actually seen diving steer kids towards a better path in life. Even better, it is something they can share with the adults in their life, which as all parents know, can be a difficult thing to find.
You need to be honest with yourself about two things:
1. Is she physically and mentally capable of dealing with the situation? From your description of her swimming, she sounds very comfortable in the water. How about the mental aspects? Does she understand the implications of the risks? Does she have a sense of her own mortality? Some kids think they are indestructable, that "it" can never happen to them.
2. Are you capable of being a appropriate buddy to her? Are your own skills at a level you would be comfortable with dealing with any situation underwater? They need to be.
This is no place for false pride in your child, but if she and you meet these criteria, I strongly urge you to do it.
PADI has a great book entitled "Children and Scuba Diving: A Resource Guide for Instructors and Parents". Your LDS should be able to get it for you.
Good Luck,
Adam