go for it, use it,
but it is a little late more mid early 19th cent, to retro it add a foot plate at the rear for the storage, change the wheel size to a larger wheels (artillery sets) shift the axles further apart (either side of the cabin) add leaf springs to the front to rear , move the horses further forward and add a central drive shaft and off side shaft, and harness for the horses also add another paair of horses, and lower the coach drivers seat.........only if you want to.
closer to what you need

rear horse harness (note the shaft is for a light buggy so ignore this)

rear near side, lead near and off side horse harness

above view
