I would probably opt to make a large pillow case to hold the quilt, perhaps out of remnants of the quilt's fabrics. (This could come in handy later if repairs need to be made to the quilt.) I would fold the quilt especially carefully to fit inside the pillowcase. There are some websites that show decorative ways to fold a quilt, including folding on the bias (which reduces stress on the fibers).
Another option would be to find an empty cardboard fabric roll for decorator fabrics (perhaps from JoAnn's?), fold and roll the quilt on that, and make a decorative cover for the roll. I think that would be harder to do, though, plus the roll would be quite long and possibly difficult to fit into a car.