Not being a Confederate command, the 3rd Georgia State Cavalry was not the same as the 3rd Georgia Cavalry, so you want to be clear about that in your notes.
The company organized under state authority on Aug. 20, 1863, Carnesville GA. Officers and men appear to have been Franklin County residents exempt from Confederate military service for one reason or another, usually age. Gov. Brown called the company into service on Sept. 15, 1863. The company's area of duty was defined as the 6th and 9th Congressional Districts; Lincoln, Wilkes, Columbia, Warren and Richmond Counties. After camping near Savannah for a few months, members were released from duty on Jan. 31, 1864.