Suggest first project is a 4-patch with plain square blocks between the 4 patch blocks. Easy, peasy. Also, If you can get have your grand daughter visit for a weekend, that will be plenty of time to get her acquainted with the machine and the very basics of stitching. It can be your 'quilting retreat'!
While you are not asking about which sewing machine to get your grand daughter, I will chime in with others who have advised about the right machine for the job. You can get inexpensive Brother machines for less than $100, and it could be shipped to the Walmart nearest your grand daughter for free. Amazon probably has them as well. Of course, you know the family dynamics and we don't. So feel free to ignore us!
Also consider cutting fabric and pressing fabric - in my opinion, a child needs to be supervised during these activities. Ask you daughter or her husband about supervising pressing - only for safety reasons, not for instructional purposes.
Some pre-cuts, along with a decent scissors and thread are good accessories to add to the package.
Oh, one more thought...you can conference your DGD in via phone or computer for lessons and learning.
Happy sewing fun!