If you have back issues, you will want to spend the money for a decent riding cart (2-wheel) or carriage (4-wheeled). Jolting along in the springless, no-back support, cheap metal vehicles most minis pull, is going to take ALL the fun away. Even on firm ground, springs under your seat help a LOT with the ride you get.
Has she dragged things like small tires? The tire, maybe from the very small cars, spare from a regular car, is not much weight, but the drag resistance is going to be helpful in muscle development when she is out on the long lines. Maybe when she is a bit stronger, you can work with two linked small tires, to add more muscle to her. Nothing heavy enough that she is pulling with her front legs, clawing her way forward. Not pretty in a "light, floating" driving animal. You moving around inside her long-line circles should not be painful to your back problems in most cases. She needs to know how to MOVE INTO pressure, be confident with weighty load, not back off when asked to really pull, like with the cart and passenger. I never advise pulling logs or fence posts, they jump, snag on things and roll. Tires on their sides are much safer, soft too.
If she is ready to hook, takes weight, knows her commands well, then I would get my cart out and hook her. She will probably think the empty cart is nothing! You could add weight to the cart as you walk behind or climb in yourself if you think she is ready. Having a header with a halter and lead on mini is always good for safety the first few rides in the cart. Driver gives all directions, voice, reins, header is just there if mini is confused. Keep your time riding in the cart short, she will be using new muscles and has to develop them.
Do make sure mini has a nice saddle in harness with a TREE inside. This means the saddle/backpad is NOT flexible, but rigid to keep any harness or weight off her spine. Most mini harness does not have a tree in the saddle.
Have you glanced thru the FACS at the beginning of the Driving topics? Lots of good information there. Might touch some things you have not thought of yet, but are useful!
I would get mini working well in the cart, responsive to commands, reins, whip touches, before worrying about much conditioning. As you get her better with those things, you will be building fitness slowly and carefully. With any new driving animal, you have to build confidence that they can move the load behind, last just a few steps more in this gait than they did yesterday. It takes quite a while before driven animal will believe you on that! With the short drives to start, you could add on 10 minutes every week or so, gain a longer work session as she gets fitter. Do a good warm up and cool down to start and end your outings. She should enjoy her work!
I hesitate to name a weight for her to pull, either starting or as a more developed animal. 30 inches is LITTLE!! She may need a lot of encouragement as you develop her, as load of cart and passenger approaches her own weight.
I am not aware of a 4 wheel vehicle being made that *I* feel is light enough for a single mini to pull, let alone one that is only 30". In my limited experience, the 30" mini's that I personally have known or worked with are marginally capable of driving pulling a full size adult and I certainly would not drive them "cross country". They seem to do okay on flat ground on pavement or something similar but if they get into any kind of pulling situation, they struggle. The people that I know personally that tried to drive 30" minis ended up going to a pair of them. Obviously if you are a small adult (100lbs or so) and certainly if you got a hyperbyke (which truly does weigh only 20 lbs), that would be a different story.