What is now the Chattanooga National Cemetary was opened in 1863, so all Soldiers who died after that would have been buried there unless they were sent home. even if they had a seperate place for burial of smallpox victims, they would have been moved to the national cemetary after the war when the government decided to locate all identifiable the federal burials and move them into the national cemetaries.
The burial listing for Chattanooga dosen't show a George Harper so he was either sent home for burial, buried as an unknown, or his grave not located.
It's possible the army medical branch may still have records archived somewhere, check on line for their history branch. I know the Army medical corp maintains a Museum so they might have them around somewhere.