Dr. Massey, the unit in question is the 1st Battalion Arkansas Cavalry, a very interesting battalion recruited in northwest Arkansas very early in the war. Pvt. James W. Brandenburg enlisted in Company D at Fayetteville, Arkansas, on October 26, 1861.

The battalion was first commanded by Maj. William H. Brooks, succeeded by Lieut. Col. Erasmus Irving Stirman. "Ras" Stirman commanded the unit for most of the war. In April 1862 it was transferred to Mississippi, where it was dismounted and served as infantry. For a short time it was increased to a regiment by the addition of some Texas companies, and redesignated as the 1st Regiment Arkansas Sharpshooters. By the time it was pulled into the Vicksburg garrison, during the siege of that place, it had been reduced to a battalion again. After the surrender of Vicksburg, the battalion was exchanged back in Arkansas, and served for the rest of the war in the Trans-Mississippi Army.

The battalion's records were lost or destroyed at Vicksburg, so there's not much service information on the individual soldiers. However, Stirman's outfit was sort of an elite unit, and you should be able to Google a lost of information about it.

The companies were from Crawford, Pope, Scott and Washington counties.