I would get some expert input. I'm no expert in time frames for fabrics, but I'm thinking the fabrics aren't as old as 1920 . It's a beautiful quilt, and if the damage is confined to the back side, I'd probably add a new backing. I'd try to hand stitch back together any seams on the front that are damaged.
My great-grandmother's quilts didn't have batting in them either (1900-1940s). They seemed to have pieces of flannel inside. Some had an old wool blanket inside.