We travel extensively over the Atlantic with our dog, but he's small enough to go with us in the cabin. We always stop on the East Coast for a night to give him a break, and I would recommend the same to others.
Having said that, the OP and his dog are on a different path using cargo shipping. I'm not sure the same logic would apply, and if I were him, I would talk to others who have used the cargo method for overseas travel.