Colin,
I checked the Illinois Rosters (Where most of the Guards at Camp Douglas came from) and I was able to find five Robert McKee's. None served at Camp Douglas. There was Robert in the 46th Infantry, Robert in the 101 Infantry, Robert G B in the 120th Infantry, Robert J in the 50th Infantry, and Robert M in the 111th Infantry.
The first Robert was enlisted at Camp Butler in 1861 and as you may or may not know served as a POW camp after Ft. Donelson, but this Robert was at Ft. Donelson. If he is your relative, perhaps he was able to rescue Gauley there if that was where Gualey was taken prisoner. Just a thought.
Frank