Your daughter may have a hormone imbalance and could be going thru early puberty. Have her checked out by your doctor.
As for her excessive facial hair, I heard on NPR that if you start waxing unwanted hair before 12, you will stunt the growth of the hair in that area FOR LIFE! So you would be doing her a favor by doing it early so that it won't be as thick for the rest of her life. She will thank you for that. Think about it, if you are doing it, she will do it eventually. What woman wants to have a unibrow or hairy upper lip? In middle school they will tease her. Girls are cruel, like it or not, it is what it is. All you are doing is postponing the inevidiable. Please don't send her to school like that at her age.
Research studies have proven that if you do it early it won't be as bad later. But once you miss that window of opportunity, it is gone forever. If she is hairy at 7, imagine what she will look like at 16.
I worked with a summer intern that was 20 YO and she had a beard, mustash and the hairyist arms I have ever seen on a woman. I was shocked!
You are not entering your daughter into a beauty contest you are trying to spare her a life of shaving her face. Sure it will hurt, but she will have to endure all kinds of agony for the sake of womanly beauty. We all do. Yes we want all girls to love the body they have. We fix crooked teeth and fix lazy eyes. If the facial hair is too much, wax it off.