This is Hunter's record in Andrew Booth's books on Louisiana Confederates:
Hunter, J. W., Pvt. Co. E, 2nd La. Inf. En. May 9, 1861, New Orleans, La. Roll to June 30, 1861, Absent. Rolls July, 1861, to June, 1862, Present. Roll for July and Aug., 1862, Transfd. to 21st Regt. of Miss., July 5, 1862.
Company E, 2nd Louisiana Infantry, was raised in Vernon Parish. There may be some clue in his full military service records at the National Archives on why he transferred to the 21st Mississippi. He likely had a relative in the latter unit.