First, major congratulations on your baby!!!
And good for you, for just jumping right in with your first quilt. What's the worst that could happen? It's just fabric, batting, and thread. If something happens to it, you'll make another.
Your quilt is adorable! Stitch-in-the-ditch and echo quilting will look really nice and will make the characters stand out. Yes, I do think you want to quilt in the character's belly. That's a lot of negative space, and if you leave it unquilted, I don't think you'll be happy with the way the fabric looks. I suggest doing barrel-shaped quilting that will add to the illusion that his belly is round. I loved Nan's suggestion of the rays extending outward from the characters.