Do you have copies of the soldier's military service file or a widow's pension application?
You can find general histories as well as more detailed chapters like the second link, describing Forrest's raid on Murfreesboro. The 1st Georgia Cavalry was involved in this small unit action.
If you limit your search for company level data, you probably will come back empty. If the scope is open a little wider, you're more likely to hit the target.