Well I can't find anything on the John H Done?? or any other info regarding what boat they sailed down the Miss R on to Vicksburg. It maybe in some of the records related to prisoners but it would take a while to go through them and find it.
However, I do know that he was discharged on Oct 5, 1862 for being of non-conscriptable age (he would have been 37-38) and exempt. It appears he went on home and by 1870 was in Arkadelphia. He evidently did not serve in any other capacity during the war that is found. He could have possibly served in some Home Guard or militia unit but there are no records to show this.