We LOVE to photograph babies. The whole staff gets excited when we have a baby session. Be warned, it takes lots of patience and time, especially, with newborns, We reserve about 2 hours to accommodate for feedings and to allow Dad to show off his skills at diaper changing.
Couple of helpful tips: Its been my experience, that babies always seem to do better in the morning. As for clothing... simplier the better. Fancy collars, ruffles and decorative designs tend to get in the way as they squirm.
Personally, I think there is nothing more beautiful than baby's skin. In fact, our best selling portraits are those taken of children 6 months or younger, with little or no clothes.