My dogs are large, 35kgs, and 60kgs, a Jack Russell is smaller and more portable if you have to carry him. And less food and water. I swear taking my dogs on multi day hikes takes more planning than putting a man on the man. Even a one day hike means I have to carry a ton of water.
I am working out how to walk the length of NZ with my smaller dog. (The larger one wouldn't be able to do it, his feet are more tender). I think it will mean early starts, walking in winter (great for her not for me) maybe me towing a trailer I can put her in when she's had enough, and us tenting and roughing. I will do some test walks of two - three days first. At least I know that in my own country I can bail, and get her collected if it doesnt work out.
This is a post I wrote a year ago on a similar thread
I guess if you live close by, have transport arranged, by car etc - not public transport, and are prepared to sleep outside - you could do it. If it gets too hard you can always bail and have them collected.
I have two dogs that love to walk with me, but they prefer to run ahead, smell, investigate stuff, pee on things, chase birds and rabbits, - generally behave like dogs - especially off lead. Walking on hard hot tarmac or sharp gravel hour after hour, day after day, would not really be their idea of fun. They would try to though, because they want to be with me.
I take my smaller one with me sometimes when I'm training for a longer walk or event. She can happily do about 3 hours max, 15-17 kms. She doesn't like wearing boots, and I have to try and find grass, sand or soft surfaces for her to walk on. Not always easy. With New Zealand having a lot of endangered flightless birds, walking through bush tracks with dogs is usually not permitted. And during daylight saving time, we have to be off the city beaches by 10am.
This year I've had to watch her like a hawk on coastal walks, because with the warm summer, we had some poisonous algae that made her vomit for a week.
We have to leave early in the morning in the dark, to keep her cool, I have to carry kilos of water for her and a bowl. And at the 3 hour mark, I have to ring my husband and get her collected. At that point she's happy to jump in the car, while I continue on.
She sees me putting my walking shoes on, and she really wants to join me, but taking her requires a lot of route planning, tide coordination, a 5am start, someone to collect her, and I have to carry a lot more weight than I like to.