David, just think how delighted your Granny must be that you still love her quilt so much after all of these years! I'm sure as you use all the great suggestions for repairing it, you will be putting a smile on her face.
Here is a video showing the whip stitch. There are several available. Look around until you find one you like.
http://www.youtube.com/watch?v=v9kGyZDWZcA