Trust me, you do not want a carriage that is not cut under, and old buggies require regular maintenance, with old tools. There are leather coils in those hubs that have to be greased and replaced, or your wheel will seize and fall apart.
Your auto wheels are not attached to a straight axle, there are all sorts of tie- rod ends and steering parts, so the axle stays straight, and only the wheels turn in the wheel wells.
The piano box buggy also looks pony size, and would be too small for a 14.3 horse. Hard to tell, though with no perspective in the photo.