What a wonderful family heirloom you have and how great that you want to preserve it.
When we lived in Virginia I was able to go to some of the DC area museums and see quite a few VERY old quilts. Some were missing large sections where the fabric had disintegrated. I looked at them very carefully to see what they had done to the quilts to save them from further damage.
What I noticed was tulle "netting". (I am not sure where you would buy it, but it would need to be acid free.) The netting was placed over the damaged area and then stitched around the edge and also tacked in the center if the repair area was large. You had to get VERY close to the quilt to even see the netting.
You will also need some good quality muslin for other areas.
Here are a few articles on antique quilt repair that may help you
Good luck and let us know how it goes.