I bring a few necessary items. A beanbag for positioning and soft blankets for each family. I don't bring things like hats or headbands. There are a few reasons for this. Firstly, I like to keep things simple and timeless. Your baby, beautifully photographed, is what you will love in years to come.
Secondly, I photograph many new babies and I love the uniqueness of each of my photo sessions. I don't want to use the same hats, wraps, headbands on different babies. It's just my preference. By all means, if you have props you like, have them ready and we will use them :-)