Mahlon, I believe Bob Meeks is correct. Andrew J. McDonald served in Co. G, 4th Arkansas Infantry, until he was dropped from the rolls with the notation, "transferred to the army west of the Mississippi River." He was one of many Arkansas soldiers who were back in Arkansas for one reason or another, and detained here. I *think* he was attached to Trader's Arkansas Cavalry Battalion (later increased to a regiment -- Newton's Arkansas Cavalry), but I can't confirm that as yet. This man was born c1824 in Alabama, a resident of Pike County, Arkansas, and later moved to Oklahoma.
I'm sure this is the man whose grave you found, but I can't say that for 100 percent certain.