DearCustomer thankyou for your question.
Generally children pull out their hair when there is stress and the anxiety is more than they can handle.
If this child has just started school or is going through some extra stress at home (it happens to all of us from time to time )and didn't pull out her hair before then you may want to get her to a dr.who can help decide if she needs some temporary medication to get her through.
Getting her a very short hair cut may not give her so much leverage like she has with say 4-8 inches of hair and may make her not so successful in pulling out the hair. However if you do this it should be because you love her eyes and want to see them more or you know it will make her look taller or whatever wonderful thing she will enjoy. Should she get a shorter haircut then a new habit may take place. It's really best to get a dr.to help you and decide if she could benefit from medication.
Here's a website with more suggestions:
Mental Help Net - Perspectives - Vol. 5, No. 4 - The Trichee
Usually the following website is used by teen hair pulleres but if your child continues you may want to at least check this out.
Hope for hair pullers. Support & tips. Pull free? Can be!