The felted wool I have worked with was only in wallhangings. I found this site with vintage quilts for sale & reading it, they appear to be backed with cotton fabrics.
http://www.rockymountainquilts.com/f...uilts_wool.php
I have also made small felted wool candle mats & they were backed with a wool piece the same shape as the front & then blanket stitched together around the edges.
How large is your quilt?