When i can get it, I use the thinnest fleece that Walmart sells. It's so lightweight that a toddler can easily tote the quilt around. And it drapes extremely well. If you haven't used it before, though, it can be difficult to use. If you decide to use it, position it WOF as that is usually far less stretchy than length of fabric.
Otherwise, I use an 80/20 cotton/poly batting. Although I haven't tried it, a pre-washed/dried white/natural flannel would probably work well, too.