I would finish the sandwich, quilt it, and then put on the eyelet. Place the raw edge of eyelet even with the raw edge of the quilt. Sew that on with a strip of fabric that will match the back. One inch wide would do it. Then turn the seam to the back and sew down that strip of fabric as a facing.
And I wouldn't worry about eyelet holes. They are too small for fingers to get caught in.