I am working on a bachelors degree online and I would not want to try to do this while traveling. When I take exams there is a proctor who watches over webcam and there cannot be anyone else in the room, or any noise in the background. This would be hard to do while traveling.
Even just studying would be difficult - most course materials are not available offline, or require a lot of online research, so it would be a hassle to reliably find a quiet place to use electricity and wifi to study. Yeah, there's libraries and whatnot, but do you really just want to go on a nationwide library tour?
It would also add a lot of stress and take some of the fun and freedom out of traveling. I'm sure you could make it happen if you really want to, but I'd wait until you're settled.