I would strongly consider an electric cargo bike. Look into what dogs need as the pavement will wear them down quickly. Where do you plan to camp each night? The southeast is not that welcoming to stealth camping and trying to camp stealthily with two large dogs will be difficult. You most likely will have to carry food with you since you plan to only do 5-10 miles per day since a lot of grocery stores are more than 10 miles apart in the rural areas.