for songs about babies, see John Denver's "For Bobbie" - Mary Travers knocks me out with it, but I'm awfully old & sentimental.

my kids always loved to hear Tom Paxton's "Marvelous Toy" - I suspect because of the "Zip, bop, whir-r-r-r" stuff. Also Loggin's "House at Pooh Corner"; there's a song-tale Pete Seeger used to do about a giant called "Abba YoYo" that has a nifty nonsense chorus that kids can wrap themselves around when they're very young. Sooner or later I suppose you'll have to deal with "Puff" but there's no need to rush it....Shel Siverstein is a treasure trove of stuff kids like, but maybe not 'til they're a little older (my 9 year old has just discovered "Light in the Attic" and is bowled over by it)