The 1860 census might very well verify this man.
Good hunting,
George Martin
W. E. O. Fuller. Private Company H, 17th Louisiana Infantry, enlisted at Camp Benjamin, Louisiana January 12, 1862, died in [hospital?] at Jackson, Mississippi May 26, 1862
Camp Benjamin, Louisiana (CS) - A Confederate camp established late in 1861 and named for Judah P. Benjamin, the Secretary of War and a Louisianian, located on Gentilly Road in Orleans Parish not far east of Pontchartrain Railroad. In January 1862 the 16th, 17th, 18th, 19th and the 20th Regiments of La. Vol. Infantry comprising a brigade under Gen. Daniel Ruggles were at the camp before leaving to join the Confederate forces in Tennessee.
http://members.tripod.com/j_richard/18th_history_camps_forts.html
The record of events for this company shows them stationed at Edwards Depot, Jackson, Mississippi on May 23, 1862.
Delhi looks to be one Parish to the East of Quachita.
The 17th Louisiana Infantry Regiment was organized at Camp Moore, Louisiana, in September, 1861. Its members were recruited from the parishes of Ouachita, Sabine, Catahoula, Plaquemines, Orleans, Caddo, Bossier, Morehouse, and Claiborne. The unit fought at Shiloh and in July, 1862, contained 27 officers and 373 men. It was assigned to Baldwin's Brigade in the Department of the Mississippi and East Louisiana, it lost 2 killed 10 wounded, and 1 missing at Chickasaw Bayou, then was captured at Vicksburg on July 4, 1863. Exchanged and reorganized, the regiment was placed in A. Thomas' Brigade, Trans-Mississippi Department, and engaged the Federals within the boundaries of Louisiana. Early in 1865 it disbanded. The field officers were Colonels S.S. Heard and Robert Richardson: Lieutenant Colonels Charles Jones and Madison Rogers; and Majors Roberts B. Jones, William A. Maddox, William A. Redditt, and David W. Self.