I agree that a backing to the pieced top would be better than none and it would be simple to do it by the birthing method. You also may want to sew ties or velcro into the inside corners of the cover to keep the comforter from sliding around inside. Here are a couple of sites that have directions for making duvet covers.
http://www.alternative-windows.com/duvet-covers.htm http://www.allfreecrafts.com/sewing/duvet-cover.shtml This is a project that has long (too long!) been on my list of things to do. I'm eager to hear how it works out for you.