I would agree you will wish to change the reins down from the rein terrets on the backpad, to run reins thru the shaft loops on her sides. You want to “keep the horse between the lines” so she can’t turn quickly UNDER the reins on her back and get tangled. One spin and you “have lost control” and she will continue to tangle badly with you being unable to stop her. Lines down lower control both her body, rear end AND prevent losing control in turns, not allowing a spin. You can drop the outside rein if needed, but not lose the animal by keeping a hold with the inside rein if she acts very silly for some reason.
As Drive NJ mentioned, adding your breeching for each practice will be helpful to the horse. If your holdback straps on the breeching are too short, maybe a double-ended snap on that buckle, will allow you to snap them to breastcollar buckle. Might add a bit of binder twine if she is long bodied to allow snapping parts together. You don’t want it real tight to start, but she is feeling breeching as she moves. This gives her a more consistant feel of both the breastcollar and breeching, to work out being ticklish for the new driving animal. You can tighten a bit for short sessions in a lesson, then loosen it again. Breeching will be pushing on her steadily for stopping her vehicle, going down hills, so she must take the pressure without kicking or running from the feel. Breeching will need to push her rump, before cart rolls forward enough to hit her hindend!! Too loose a breeching fit, cart hitting horse will cause a wreck. Too tight a breeching, may rub her hair off, so you want a nice medium-snug fitting breeching on the animal. Getting the tickles out with no vehicle attached is best for everyone!
I agree also, with taking your time to be sure she is comfortable with each thing you add or introduce her to. Make sure she is bored with them before adding more things. I agree with RAH about the blinker fit, wide as possible, and trim off the long hairs around the eye. Some horses do better with snug fit blinkers, but she has been worked open already, sounds pretty nice minded. So let her look with open blinkers. They are really to prevent her from reading your body language and “help” you because she KNOWS the routine. She must ALWAYS WAIT for the command, before doing anything while hitched because she is NOT ALLOWED to make choices. DRIVER makes the choices of when and how, horse must wait for directions. Can’t have two “Captains of the ship” doing the driving, horse gets NO vote!
You may want to latex wrap her bit, soften the feel, because with Driving she will need to take a bit of rein pressure in her mouth. You do NOT want her being too light to the reins, over-responsive in a carriage. The distance of reins from hands to mouth, adds a LOT of leverage and rein weight on her mouth. Way more than a ridden horse gets. She should take a bit of rein pressure, give her face, when you ask her to do things. Giving her face (nose dropping, face vertical) for very short times, will begin to aid her in using her rear quarters better for balance of the entire body. This asking is a building process, short asking sessions during a work, will not be learned in just a short time. I am old-school in believing ring sided bits (direct-pull), are a training step towards a leverage (curb) bit on a trained/more finished, horse. I can do a lot more with my horses in curb bits, because they are better balanced, responsive in a different (NOT FORCED) way than I can get with ring-sided bits. I want my horses “talking back” with my rein requests by taking pressure, self collected or hunting the bit, going long if given extra length of reins. I NEVER want that head flying up because I picked up the reins and felt her mouth, or having horse put chin-on-chest to hide from the bit and rein pressure. That is too light a horse, shows me an untrained mouth, not truly a “soft mouth”.
And lastly, it looks like your harness saddle has what we call a “sliding backband” to hold your shaft loops. This backband allows the strap holding shaft loops to slide side-to-side for shafts and carriage on uneven ground. You will want to make sure the strap is well conditioned, slides easily, so one side shaft doesn’t get stuck up or down when horse is finally hitched to a carriage. Such a harness saddle is all right for SOLID shafts of a 2-wheel cart, a set of buggy shafts, but NEVER used with independent shafts. The ability to have shaft loop slide up, will let the Independent shafts on a 4-wheeler to get uneven and cause a problem. This is REALLY important to prevent an accident or wreck with the horse.
The solid shafts of a 2-wheel cart are supposed to pull the (well-conditioned) sliding backband back to even when the ground levels out. Independent shafts can’t do that with the hinge in them, will NEVER self-level. So you could end up with a shaft over her back, other poking her in the elbow or stomach, horse getting upset with that. We have a sliding backband harness saddle, and I had the sliding strap part sewn in place, so it only LOOKS like it slides. A friend of ours had her sliding strap part stick uneven after getting back on level ground and horse got poked pretty good with crooked shafts on a turn. I didn’t want that to happen to us, so we have “the traditional look” but no chance of a problem.