There is a website you can check out, Buggy Bob's. This is a company in Shelbyville, TN that sells many varieties of carts and carriages. They are pretty expensive, but you can look at what they offer, and you can buy kits and also most parts from them. Building a cart isn't difficult, except for the wheels, and those you can buy and have shipped to you if you don't have anywhere close by that you can get them from.
You will probably want to buy the wheels, shafts, and a few other bent wood parts as those parts are all bent to shape with steam and pressure and you need special equipment to do the bending and shaping. As I said, all available, if you can find them. We get our parts from Amish buggy makers, but they generally don't do much on line. They will ship parts to you if you can find them.
A good friend of mine here in Wisconsin builds carts, and has built several for me. I actually have one in my basement right now, he built all the components (or we bought them) and I am in the process of doing the finish work, sanding, staining, varnish/clearcoat etc. I wish you were closer to WI, as I am doing this cart for sale, and would happily sell it cheap to someone who wanted to do the finishing themselves.
It is very rewarding to be able to see a cart you built yourself in a competition, and particularly if it does well for you. We use our wood wheeled carts in all types of competitions. We primarily show in ADS shows, which require wood wheels in most cases, but we've shown in mini breed shows with them and usually are the only wood wheels in the class. We usually place well, but do have a little trouble sometimes with some arenas if they are too soft and deep sand. ADS shows usually run on grass, so the narrow wheels don't cut in. We did build one fine harness cart with interchangeable wheels, wood for the carriage shows and pneumatic bicycle type wheels for the soft arenas. Jerald used to offer both types interchangable on their carts but I recently was told they no longer offer wood as they were too expensive.
Spend some time on line, and see what you can find, its out there, but not easy to find and the shipping is expensive. Wheels are heavy, and the shafts alone are anywhere from 4 to 8 feet long, so good luck.
If you want to send me a personal email, I may be able to point you in the right direction.
[email protected]
, but in mini's I wouldn't think you could even get too short with dragging on the ground. 
