The regiment was first organized in the Trans-Mississippi Department during the winter of 1863-64, as Harrison’s Battalion Louisiana Cavalry
The regiment saw little, if any, fighting during the war. Most of its service consisted of courier and guard duty around Shreveport and Alexandria. Individual companies of the regiment may have conducted independent campaigns against deserters, draft dodgers, and Jayhawkers in northern and western Louisiana.
6th Regiment Volunteer Cavalry
Here is an old thread discussing the regiment which may provide more detailed history: