First of all, since you are the owner of this quilt, it is completely up to you to decide what you want to do with it. If you want to quilt it, you need to use the same type (not age) of thread that it was pieced with and you should use a backing of the same vintage/fabric type so you don't negate the value of the quilt top. I am assuming here that it is a cotton quilt......?
Restorers repair and re-quilt antique quilts all the time, it depends on what repairs are needed on the specific quilt. It's not uncommon for them to work on quilts from the 1800's and earlier. Fabrics of this vintage are still available today.
I would look over each piece of fabric and all of the seams to make sure there are no repairs needed there. If there are some block pieces that need to be repaired, PM me and I'll tell you the best way to go about making the repairs. In my opinion the quilt top should be quilted to help add to the stability of the pieced top...as long as the top is in good condition and not disintegrating. If the condition is less than good, I suggest you just do your best to display it properly and enjoy having something that your grandmother made in your home. There are several good articles on the net on how to clean, store and display antique quilts. Good Luck!
Rose, a quilt restoration student