Part of the enjoyment of being a new parent is splurging on your first baby, filling their stocking is more for the parent's fun than the child, but it is an easy way to give small gifts. It's also a way for new parents to start their own traditions.
This year the baby in my family is my fifth and I still will fill his stocking because all of my other kids would not understand why Santa would fill theirs and not his, they would think that wasn't fair and would actually be quite upset. I have always done this with my kids. I don't spend alot and I usually try to get them things they need, like someone's suggestion of sippy cups and snacks.