As MFord said, you can just take the binding off and use any one of the quilt as you go methods to add an additional border. I'm doing that for a friend of mine with the same new bed issue. Take binding off, take new border fabric and lay right side down on quilt, take backing and do the same (place on back of quilt, right side facing quilt). Match all the edges, pin really well, sew a seam thru new backing, quilt and new border. Press new border & backing into position. Cut a new piece of batting & butt up against quilt. You could whip stitch the new batting in place or just make sure that you quilt pretty heavily over it. Quilt new border & rebind.