I am happy to help you with this!
First, it is always a good idea to have a bridle and driving lines on any hitched animal, as shared above. That's for safety sake. If a horse or pony is hitched to a vehicle there needs to be a person in the cart with the lines in hand.
Next I would raise the breast collar at least one hole on each side. As it is now it is laying across the point of her shoulder which is where a little bundle of nerves lay. So driving with the breast collar this low could be painful.
Another thing to consider is to bring that neck strap back and hook it to the waterhook on the saddle. If you do this then you won't need to raise it, as bringing it back will raise it. You can attach it to the water hook with a small loop of twine or get a neck collar connector strap. Here is a photo of what that will look like:
View attachment 42489
The rest of the harness look like it is adjusted well!
As for the cart, as it sits right now the shafts are too low. They should be running more along the middle of her body, in line with where the traces come off the breast collar. Because your breast collar is adjusted too low, your traces are also running too low. To fix that I would raise your shaft loops maybe as much as two holes. Then you will have to readjust your balance, most likely by sliding your seat forward. This cart is a good example of why the curved shafts (as shown in the photo I shared above) are nice. They allow the front of the cart to stay level while reaching up to the shaft loops. I think you'll be able to get your dash and floor level through moving that stablizer bar at the back of the shafts, the part that connects from the shafts to the floor. Here is a blog about doing that: Balancing the Easy Entry Cart Part Two
This page (best viewed on a computer) has a few blogs about balancing an easy entry cart: VEHICLES | The Essential Horse | Driving Horses | Driving Ponies
Great job hitching!! I know it's confusing when we are starting out. I would say you have a good grasp of it, with a few tweaks you will be out enjoying your pony and cart