That was me when I was a child!! Turns out that I have a condition called nonclassical congenital adrenal hyperplasia. People with NCAH produce excess testosterone from their adrenal glands which leads to excess hair, oily skin, early puberty, etc. It's not at all uncommon among Ashkenazi Jews, Hispanics and Italians (I'm the latter two) and it's not life-threatening in its milder forms. Doctors often miss it -- I wasn't diagnosed until I was in my 30s! See www.caresfoundation.org for more info.
There are other reasons why a little girl may have excess hair but only a pediatric endocrinologist can identify them. You should talk to your daughter's pediatrician and get a referral for an endocrinologist.