Hi, S.!
As all the other women have already said, it IS very normal. I have long hair, and I think it was around 2 or 3 months postpartum that it really started falling out -- it drove me CRAZY! It was falling out every time I turned my head, and was ending up all over me, my baby, my husband, our FOOD, our FRIENDS...!!! It was pretty much a constant annoyance until the 10th or 11th month, and slowly subsided from there. One added "bonus" (ha ha) no one has mentioned yet is that pretty soon you're going to start to notice the funny-looking "shorties" (as my hairstylist called them) that appear as all your hair starts to grow back in again around the same time. When I wore my hair up, I had this goofy, curly "fringe" along the back of my neck. Fortunately, everyone was looking at the baby, not me! :)
- L. :)