I moved abroad from the States to a Caribbean island with my dog. Like previous posters stated, it required a a series of rabies titers and a health check 24 hours before travel. Your destination country will have detailed requirements, and as long as you follow them you should be fine. I will say that you should check the airline carrier you will be traveling on. Some carriers have requirements as to landing with animals in a certain climate (heat/cold) but this may be for animals in the hold, and not in the cabin. I will admit it was one of the more stressful parts of my overseas move, but it was mostly because I couldn't travel in the cabin with my corgi and had to put her with the cargo.