Thank you Art. After receiving your response, I looked at Booth's entry. It is as follows:
Gaudet, Os., Asst. Surg. Orleans Guards Regt. La. Militia. On report for Oct. 1861 of Louisiana Legion 1st Div. Commanded by Brig. General James Trudeau, and a supplemental report of Maj. General John L. Lewis, commanding 1st Div. L.V.T.
Looks like you hit the nail on the head.