Biting one's fingers most likely refers to either biting one's fingers, but it could also be seen here as an umbrella phrase that includes sucking one's thumb. Generally young children have an oral fixation that can be triggered during times of fear or anxiety, we've all seen a child nervously suck their thumb or bite their fingers. Additionally this could mean she's so young that her mental acuity is underdeveloped to the point that she doesn't even yet know how to do something as basic as bite her fingers. Lastly, perhaps biting fingers is a crude sexual euphemism alluding to the fact that this girl is too young to be sexually mature or experienced.
