Congrats!! As for the kitty getting in with baby. . . Um, what's wrong with that? My 2 sisters and I have have cradle cats and my niece Chloe also had a cradle cat. I know little Chloe LOVES cats like nothing else and has all kinds of cat toys. I think it establishes a serious bond.
As for the folklore on cats smothering babies, show me proof. It's all wives tales. If the cat is mature and settled down there should be no problem. I wouldn't put a kitten there but I never had a problem with cats! Just saying!
To clarify I do not think there is anything wrong with cats and babies together. I also grew up with cats. But not everyone feels that way.
I've read too many threads about people dumping their cats because "the cat won't leave the baby alone" or some other similar lame reason.
If you don't mind the cat sleeping with a new born, that's lovely.

I only mentioned it in an effort to forestall a serious problem later and to help Moe, because it would be very confusing for him to suddenly be told he can't sleep in a spot he's been sleeping in for six months.
And if he is allowed to claim that cradle, then the baby is put in it, and he is told that is not his spot any more, problems could develop. It was for Moe's sake that I spoke up, not the baby's.