Foremost considerations are airline policies (if flying) and health certification. Having commercially flown with retrievers for the last 20 years, I've not once experienced anything to be concerned about. To the contrary, most US airlines take especially good care of pets. Food and water must be provided, forms signed, and extra fees paid. For what you pay to fly your dog, they should be provided a seat up top, and given a milk bone when the beverage cart comes by.
Each airline has their own pet policies and some don't allow pet travel at all. Most policies stipulate that pets may be transported only when the outside temperature is 45 to 85 degrees F, and most airlines will not fly retrievers. Outside of this range requires a veterinarian statement that you per is acclimated to these extremes. Some airlines will not fly pets as a matter of policy between mid-June and mid-September, so plan your trip to Canada accordingly. These temperature ranges generally preclude bringing retrievers to the Southern Hemisphere.
It may be winter there, but it's usually to hot here in the States during June and July - and vice versa depending on hunt timing. Fortunately, there is excellent Argentina duck hunting to be had March-May. Consider that such travel will require Fido spend 18 or so hours crated.
Be sure to bring some dog boots while Mexico brant hunting. Shell reefs will cut dog pads and there's no sense in Fido limping around on injury reserve during the trip of a lifetime.
Health certificates must be completed by a veterinarian within 14 days of pet travel. Consult your veterinarian about any special concerns for the country you'll be hunting.
Keep a leash in your pocket. You'll be required to removed your dog from the crate by TSA, and surely they'll be ready to stretch and do their business soon after departure.
During the past 20 years, it's been a joy hunting with retrievers throughout 5 Canadian Provinces, all 4 US flyways and Western Mexico. One of the most memorable events didn't involve retrieves at all. After Memphis TSA had checked her kennel crack-of-dawn early one morning, I instructed Cooper to "kennel." Much to everyone's surprise, she leapt onto the ticket counter, grinning and in full-mode spin cycle like only a young lab can, and swept the counter void of everything and then some. Off to a great start, the following week duck hunting in Manitoba was equally spectacular.
Ramsey Russell, GetDucks.com