Wonnie, I was intrigued by your question. Then I finally realized I had done some birthing when I went through a phase of making quillows for my family back in 1990s. This was long before I got into quilting.
If you Google quillow instructions or similar words, you will find useful information. Just ignore the instructions for adding a pillow. Binding was not used, but simple straight line quilting with a walking foot will work well.
I liked a couple of answers which suggested making a wider binding strip and avoiding stitching through all the layers this way. Why not try making a few quilt sandwiches and try out the binding in different ways to see if you want to go this route?
Good luck and enjoy!