Measure your pony, to know the sizes you need. Many might call your pony a “cob” for height, but she may not measure that way to fit harness. My friend has that issue with his Arab cross ponies, not enough bulk, though similar to yours in height. Looks can be deceiving, which is why you use a quilting tape measure and write things down. Ideal fitting is in the center hole of each strap, but animals gain and lose weight over winter, working and getting fit. So having extra holes is real helpful. Anything in the “last hole” either tightened or loosened (unless equine is obese), is not a good fit. With new harness, you can send back too small or large pieces, get a different size. Can’t do that with used, so measuring right before buying is important.
You will not need any kind of checkrein, not allowed in Combined Driving. No they are “not safety devices”.
I would suggest a kicking strap with a newly trained driving horse. It goes over the hip or croup, depending on design. Strap ends wrap around shafts to help hold down the rump. Weight of driver, cart is HEAVY at that leverage point, very discouraging to horse trying to lift rump to kick for whatever reason. Few horses ever try kicking after the first effort. Most never try, but having the strap on, can prevent problems while still in the learning stages. You can always resell it later to another green horse owner!
Do you ride? Have a favorite pair of reins? You want to drive with reins that fit your hands, are comfortable to hold for long times. Try a bunch for size if you don’t know your rein size. Many women have little hands, so 1" or even 3/4" are just too wide. Plus some are extremely thick leather, making them uncomfortable between your fingers. You want reins long enough to sit on in the cart. Too short have you “reaching forward, leaning” which is an uncomfortable body position to maintain very long. Bit end should have buckles to attach with, NEVER snaps. Snaps are cast metal, can break easily. Worse is how they rattle constantly, metal to metal, on the bit. I once heard it compared to someone banging a spoon on your teeth, all the time yiou drive. The leather billet on rein are soft, you SEE AND FEEL the wear in leather each time you put them on or off. This helps prrevent accidents with handling the billets. Rein ends get lots of wear, wet from horse saliva, rubbing the bit.
Synthetic harness is fine to start with. There are a number of sites selling driving things on Facebook. Harness, vehicles, odds and ends. I would avoid the India type names, no one seems to know anything about the sellers, so we are not sure of the quality of their goods. Plus hard to return!
Biothane is a trade name for a certain kind of straps. I don’t really care for it with hard edges, too shiny of a plastic look. Other kinds of strapping are the beta-bio, some of which look and almost feel like leather. Soft edges, matte finish in black and brown, various colors discussed in another post. Ideal and Zilco seem to have a different strap goods than the American/Amish makers. Both are good brand names too. The quality of the hardware is very important, with stainless steel working the best in strength and easy care. You DEPEND on the strength of stainless buckle tongue to hold firm in stress situations. Never buy brass or wire tongues on buckles for horse use, they bend or fold, letting straps loose in stress.
See how pony does in training, before investing in a vehicle. Have to say that your tastes change as you learn more about driving! I thought our Runabout was very cool until we bought a Trap! Ride along with others if you can, see how various vehicles ride, turn, ease of use.
You might read thru some of the “stickies” at the top of this forum. Tons of helpful information in there to absorb, consider as you get deeper into driving. Welcome to the group!