It could be a fungal infection, like yeast, or some sort of allergy. Definitely ask the doctor before using a medicated shampoo on her scalp (although if that's the case with her, it's probably exactly what they will recommend.)
If it's not a medical skin condition, you could try a few other things. What about a light misting of a detangling spray when you are combing through? That way you get the conditioning on the hair and the scalp is not affected because the ends are treated.
& when you say "break" do you mean pull out of the scalp roots and all, or brittle/breaks mid-hair? Is it curly? Do you use a wide-toothed comb on it when it is wet? Or do you wait until it's dry to brush it out? Curly hair is more brittle because of the shape of the strand. If it falls out at the roots when you brush it, there is probably a fungal thing going on or a diet thing that needs to be examined. If it's happening mid-strand, she may just have some brittle hair and she's very young, so she might grow out of it. If it's persistently brittle hair, that's another thing to bug the doc about and see if there is something you could do to improve the hair follicle from the roots, since the rest of the hair is already dead and there's nothing you can do to really improve the "strength" of hair once it's visible. But keeping the cuticle of the hair strong may require a combination of methods if you are really worried about it.