I started losing hair by the handfuls when my first was 4 months old. It continued for about two months. This is totally normal.
I exclusively breastfed for the first six months so breastfeeding did not keep it from happening to me.
Incidently the losing of the hair started right when I got my first menstral cycle - so it was very obvious that it was all hormones.
However, I was concerned about losing my hair after a solid month of it so I went to the doc and asked for a thyroid panel. Hypo and hyper thryroidism runs deep and wide on my father's side so I wanted to be sure. Turns out everything was fine, but after the test I was much less apprehensive.