That looks correct, according to the muzzle at least. A nice Confederate cannon, copying an early Parrot gun (the muzzle swell is the big giveaway). Watervillet Arsenal carriage is interesting, makes you wonder if the carriage it's Confederate vintage or a period carriage paired with the gun. Original carriages are indeed rare, many have rotted in outdoor displays, although you would be amazed at what certain pieces of wood will weather the ages.
With Civil War era guns, since all the carriages are of a standard pattern, widely produced, there are more survivors. Earlier cannons, not so much.