Hang onto the yarn you have for a hat or some handwarmers for yourself. It's pretty yarn and will do nicely on bigger needles--I bet it's kinda stiff on the little ones.
Since you're new, I'd stay away from any bumpy yarn like Baby Boucle or whatever. Look for a thin, smooth yarn that may actually say "Baby" on the label. As someone else said, sock yarn is about the same weight.