Its a little challenging to travel with a dog, especially as a kayaker but I wouldn't trade it for anything. Like gh said a good dog is a friend for life and a great travel partner. Having a truck with a camper shell has been huge. I even think that my dog considers the truck more his home than the 4 rooms that I have rented in the last 2 years.
On certain creek runs that have a trail like OBJ, Clear Creek of the Ark, Daisy, Pine Creek Rapid I usually let him run along the side as I boat and we both get a workout. Longer runs like Escalante, The Green, or Callaghan Creek he just hangs at the takeout and guards the beer. When he was at Skook he just hung at the rock and attracts ladies, same at Salida/BV. At Gauley he prefers the take out but you gotta back up in the shade. My dog is one of my main paddling crew and he is the man.
I can't imagine going on a road trip without him. International is a bit trickier but it can be done.
check out his adventures at www.sampsonspot.blogspot.com