Bartlett's MILITARY RECORD OF LOUISIANA, pp. 237-240, has a roster of the militia at secession.
The best source is Broadfoot's ARMY OFFICAL RECORDS SUPPLEMENT, Serial Nos. 35 and 36 (Record of Events,Volumes 23 qnd 24). The militia in the New Orleans area, and some of the other parish regiments, are posted with lists of officers.
The militia was 5 divisions with 2 brigades each. Later, when the 1st Division rose to 4 brigades, the militia was reorganized into 9 brigades, and the division commanders were dropped. In March, 1862, the 4 brigades of the old 1st Division, was mustered for PACS service in 3 brigades of State Guards, which disbanded after the fall of New Orleans. A few State Guards units remained in service. The other brigades were broken up early in 1863, when Governor Allen formed a new State Guard, which eventually numbered 5 battalions.
Some CSR's are in the National Archives, but researchers report little other data available in Louisiana archives.