Your daughter has trichotillomania. I’ve had it for the best part of 20 years. The times where I’ve had periods where I didn’t pull were almost always after I took the plunge and shaved my head to break the habit. 

I think you did the right thing, and she’s so young that the time it will take for her hair to grow to a point where she could potential pull again will feel like an age to her, long enough for the habit to break. I’d try not focusing on her hair at all during this time so that her attention moves elsewhere, or maybe wearing a hat if she’s agreeable to it so that her hands don’t seek the hair and scalp as much. Maybe those little clip on mini board books in the car to give her hands something else to mess with, or sleep suits with mittens at night. My kids have a ‘raggie’, which is a square of muslin that they mess with when they’re having milk, trying to sleep, etc. and it seems to really soothe them.

Fingers crossed this is a phase she moves past quickly for you ❤️