I have a copy of the "alterations since last return" sheet dated January, 1862. It states that Charles M. Cunningham transfered to company "I" from company "H", and died on January 8, 1862 at Burkess of measles. I think Burkess was the name of a camp, but not sure. Will have to do some more digging.
I hope this adds to your info on him.
Regards,
Dan Hyde