This condition should be evaluated by a pediatrician or pediatric dermatologist familiar with uncommon skin ailments in children. Of the syndromes listed in textbooks, your child's sounds most like this one:
Prepubertal hypertrichosis
Prepubertal hypertrichosis is seen in otherwise healthy infants and children. The distribution is generalized and becomes more obvious during childhood. There is involvement of the face, proximal extremities and back; hairs on the latter location assume an inverted fir tree pattern.
Hair removal would seem appropriate. Laser treatment can be done in young children as well. Even if the hair loss is not permanent, getting rid of a lot of it for extended periods may be worth considering. The doctor who evaluates your child will know about this too.
Best.
Dr. Rockoff