I did my first infant shoot last week, I'll post a few when I get home, and I wish I had not waited until she was two months old, however it was a very fun shoot. The leasons I learned:
Be comfortable with kids and make sure mom and dad are comfortable with you, it makes it easier when you suggest some off the wall ideas. 
As already mentioned, a good time to shoot is after a feeding and a burping. They aren't so cranky or difficult.
Be prepared for the unexpected. Mom moved the baby and a necklace the baby had fallen across her hand, it's one of my favorite images of the baby.
It helps if the child is you niece. LOL
Don't spend more than an hour or so shooting the baby. My niece didn't seem to mind too much but I started feeling a bit guilty we were shooting her so much after an hour.
There's much more to say but I'll stop. I think you'll do fine.
Jeff