Hi Jean,
Nannie Harris was my great-great-grandmother - I'm descended from Laura Johnson and William Aldridge. I recently had an ancestry.com DNA test and it came back 0% Native American. I've always been told that there was Cherokee in our family somewhere, but it appears to be rumor only. If you know of anyone else in our family who had a DNA test done, let's see if they have any Native American in their results.
Cheers!
Kelley