Trichotillomania (Hair Pulling) Support Group
Impulsive control disorder is the inability to resist an urge, temptation, or impulse, even when it may cause negative effects to the self or to others. If you or a loved one suffers from impulsive contorl disorder, join the community to find support and share your challenges with others who know what you're going through.
The response I suggested is what have been most helpful to me as a child with trich. However, every situation is different, especially because your daughter eating her hair is a health issue. Everyone here is only trying to help.
Your daughter sounds similar to me when I was young. I love long hair, but I'd pull my own. I would hide my hair anywhere I could too, and my parents tried gloves layers of scarves and hats and all.
I did have period of time I was okay though? I had started taking an adhd medicine and somehow it helped me pull less. At least until my mother got lax on making me taking and i'd "forget" to take it. Mind you that it only made me pull "less" It's not a cure.
But during that time we did a few things that helped; I saw a counselor (who seemed to help mom calm down too), I got a wig of my choosing, and as gross as it sounds we started "measuring" the amount of hair I pulled. Mom gave me a few ziploc bags and when I pulled instead of hiding the hair I would (most of the time) put it in them.( This is the reverse of what mandapanda suggested, but as a last resort might work. Please be delicate if you attempt this.)
This of course made me realize the enormity of it. Which for a child is quite a big thing to do. I felt ashamed and after awhile hated the bags and myself, but they did their job. I then started actively trying to fight myself for the first time.
I don't know you or your child personally, but possibly these things might help or they might not. I hope they do at least a little bit. Please talk with your daughter through all of this and as the others said let her help with choosing methods and talk her through processes.
Communication is important, and even if it feels like she's not listening she most likely is, but is terribly distracted by herself and her impulsiveness.
Again I hope this helps. I'd like to help any way I can.
Also it could be an ADHD habit/Asperger's or autism tic so they are important to get checked out too (I found out I have Asperger's with some ADHD traits as a 26 year old female... they just DON'T diagnose it is girls).
Also if she has these conditions, you may have to accept that at some point in her childhood/in her adult life, she may have exhausted all the options and require medication. I hated meds for so long but sometimes it is the only way to reduce the suffering. I wish I'd seen that sooner!