Greg,
I do not know for certain the names of W J Walker' s parents (what little I know has come from Ancestry and other sites, which we know are sometimes inaccurate). I have found two or three 1860 Georgia census records, each with a 15 year old W J Walker listed living with family. I plan on contacting the ADAH regarding the pension application and apparent rejection letter - unit information should be on the application.
John D Cowart