It's a nice quilt and will look very nice on display. Repairing a quilt can devalue an antique but unless you plan to bring it to the Antique Road Show or insure it, I wouldn't worry about it. I would hand sew a new cotton white binding over the existing frayed binding. That way you will prevent any further damage (vaccuum catching a raw edge). With antique repairs, I think they hand sew bridal tulle? over frayed spots for perservation.