Single Wheel Cart?

[Nanno]

A one-wheeled cart would need a set of shafts to keep itself upright, and you would have to be very careful how you loaded it in order to keep it balanced. You would also need to have your shafts battened down tight to your harness. With a two-wheeled cart you let the shafts "float" in the shaft loops to allow some wiggle room for cart maneuvering. Maneuvering a one-wheeled cart would be totally different from maneuvering a two or for-wheeled vehicle so you would want your shafts held tight to the goat with no up-and-down movement of the shafts so as to prevent the cart from being able to tilt sideways. You wouldn't need a whiffletree, traces, or britchen with a cart like that. It's so small and lightweight that you could have it pulled primarily by the saddle with a breastcollar in place to keep your saddle from being able to slide backwards. For such a small, lightweight cart a harness like this one (with a sturdy saddle pad added) would probably do:
https://llamaproducts.com/goat-harness-work-basic.html

As with any other type of cart, you would have to make sure the front-to-back balance is correct so most of the load balances over the wheel and not on your goat's back. This would be something you would have to figure out when designing your shafts. It's an interesting concept. I've never thought about anyone using a one-wheeled cart, but I supposed for rugged trails it would be similar to using a travois, only easier to pull.