I think you've gotten some good suggestions. For the tail, I'd figure out what part will hang over and sandwich it and birth it like jemma suggested. Then applique the rest of the figure. Leave about 1" to the edge of the quilt top unattached. Sandwich and quilt the rest of the quilt. Bind the quilt, keeping the tail loose. After binding, attach the tail to the edge of the binding.
As to painting, I like the look of watercolor and have experience with watercolor on paper. So I'd use dye or ink rather than acrylic paint. "Quilts of a Different Color" has some good info. Tsuniko ink has good info. I've been using Inktense and beginning to have success with it.
Love to see pictures.