your musket is a M 1816 musket of late production. You did not write whether it is in original flintlock condition or as so often converted to percussion. For original ramrod look at: Gunderson Militaria or Shiloh Relics, perhaps Osborne Lodgewood, on their replacemet part side. I can not recommend any of the repro rods, as the ones I saw during my collector life are not in original shape: the shaft is always turned cylindrical (=more simple to produce)whereas an original grows wider in muzzle direction. Also the head is mostly not in correct button shape (this was my experience;perhaps one of the other gentlemen knows a correct repro rod?). It is far better buying a shortened original rod and let it elongate by a skilled mechanic able to do welding and turning jobs and perhaps to cut the correct thread at the shaft end.

Best regards,
Marc