Kathy --
This was a company called the "Wilson Greys" recruited in Tallapoosa County AL. Here's an old message to someone else who asked about this company:
http://history-sites.com/mb/cw/alcwmb/archive_index.cgi?noframes;read=10209
It appears that D. C. Carter and several other Carters left this company and joined Co. "D", 46th Alabama Regiment.
Please reply if you're interested in copies of service files or pension applications for these men. Quite a few of these are available for Tallapoosa Carters in both regiments and perhaps others.