I have carted with my dog and have real experience with that. The original poster here, Jessy, you're desperate, but that doesn't change the fact you're also naïve and foolish. You can't justify yourself by being on a mission from God. We are justified by Christ's work, not our own and we're called to, "walk circumspectly, not as fools, but as wise, Redeeming the time, because the days are evil." "Wherefore be ye not unwise, but understanding what the will of the Lord is." (Eph. 5:15-17) I'm not tearing you down, but advising you to know and do God's will. Find out what the mission from God is and do it, and if you do that, you don't have to justify yourself to anyone.

I'll start with the weight issue because your conjecture suggests a lot of it in survival gear and other useless junk that someone who has no experience traveling light is likely to drag along. It would be good if you started traveling on foot because you will be forced to learn to travel without un-needed weight and avoid the extra ordeal of dealing with a machine and harnesses. You have foreseen how the machine and wheels will make things easier, but you have not foreseen how they will complicate travel and make it harder. Again, it would be good if you learned to travel light first, and then add the burden of the machine which might possibly increase your comfort or your daily distance if nothing goes wrong.

Dogs can pull a lot of weight, and they can pull it fairly fast. I've bike-jored with a dog, ski-jored, sledded, pulled a limber and caisson, pulled a ski-trailer, pulled a roller sled. I have a dog that pulled a 100 pound roller sled with three people on it, probably close to 400 pounds, and he would rip down the road at over 20mph. Even single dogs can pull many hundreds of pounds.

Dogs cannot brake much weight. If their harness has a breeching strap and the cart/sled has brake poles, they can brake some weight, but not much. Their legs are not like horses and they don't have the mass. This means any downhill is very dangerous for a dog in harness with weight. If you lose control, the cart or sled will run them over and it will all be over. It wouldn't take a big hill either, just an average steep driveway would be enough to creme your team. This means if you go anywhere that isn't totally flat for the entire route, you will need to be super vigilant and have control of the brakes both downhill and up. The dogs are pretty much helpless in this aspect. They can pull, they cannot push.

If you're really here for advice and not just to tell us about your fantasy, take some advice to begin traveling as soon as possible, and take as little as possible. Only add things after you're sure you cannot go farther without them. That means your first trip should probably include nothing but water. If you make it to three days of travel, bring dog food and water. You can fast yourself but drink water so you don't get dehydrated and lose better judgment. It doesn't sound like any particular distance matters to you, so just keep adding only what you need for an increasing duration of time. This way, you will learn yourself what is really necessary and what is possible and you will know without anyone telling you.

Dogs cannot take heat. They are crepuscular. From an hour after sunrise to dusk, it will probably be too hot for them to go anywhere. Making them work significantly in the heat is cruel. Don't get me wrong. I know about working dogs and I don't mind working a working dog and working them hard. But working them in the heat will destroy them. They don't sweat like horses and they just don't have any mechanism to deal with heat except to rest and work when it's cooler after and before sunrise. If they get hot, they will need water and lots of it. They can only cool by panting and they need water or saliva to evaporate in their mouth to transfer the heat. If they're dehydrated, they'll overheat fast.

If the dogs are really working, they will need to eat a ton of mostly fat. "Thou shalt not muzzle the ox when he treadeth out the corn." (Deuteronomy 25:4). How much you work your dogs will depend a lot on the heat and how much you can feed them. Paul wrote to the Thessalonians, "For even when we were with you, this we commanded you, that if any would not work, neither should he eat." For your working animals, vice-versa is true: If they don't eat, they don't work. The less you can feed them, the less you can work them. What counts for dog food is mostly fat and protein, so if the raw food you're feeding is more than half carbs and filler, you can only expect to get half the work out of them. Same thing would go for cheap commercial food. Working dogs eat a lot. A single dog on the Iditarod can eat $150 to $200 in food in 10 to 12 days. Food budgets for a single team are several thousand dollars and that's just for a couple weeks' work. A typical working dog eats about $1000 in food a year where the owner is paying a lower price for buying food in bulk (for dozens of dogs). A person paying full retail would have to pay even more. Going day-to-day makes it hard to buy in bulk whether you're buying raw or not. This could make it extraordinarily hard and costly to feed enough fuel to do significant work.

That's how you get started: one day at a time and don't take any weight that you don't need. Work the dogs only before sunrise and after sunset, longer only if it's below 40 deg. F. See what you learn and adjust your plan accordingly. If you try it, you'll get somewhere. Let us know where and what it looks like. Enjoy the tour. Take care of your partners.