George,
I have two kids in the Kid's Leagues at Allsport. The Allsport program begins with a weekend long program where the kids get their "driver's license". It's a very good program that combines some classroom time with a lot of track time. They take kids with absolutely no driving experience and develop them into fairly competent drivers in a short period of time. As Brian mentioned, it is amazing how quickly the kids learn and how instinctive their reactions are.
At age 8, your daughter will be one of the younger kids (but she won't be the youngest). This is probably the best age to start most kids since they have begun developing some coordination and they can understand the concepts of driving. While the kid's carts are adjustable, some of the smaller kids still have to be fit with quite a bit of extra padding to hold them into the seat and so they can reach the pedals.
Contact Allsport directly and they will give you all the details. Note that just like all motorsport activities, this is not a cheap "hobby". And, it's really bad when you have two kids in their program as a few of us have.