Cheri, you might really want to look into those pet shipping organizations that are listed on the site that ChrisW provided. Here is what my friend with Continental said:

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As for your friend with the pets I am afraid that if they will not fit under the seats in a pet carrier that the only way to Belize is in the cargo compartment. I can't speak for American but Continental puts pets in a climate controlled cargo area and they do not put then in until its time to leave the gate so they won't get overheated. The Capt. signs a receipt for the pets at the time of delivery to the plane and has a maximum time period the plane can be on the ground before the plane must return to the gate and the pets removed for there safety. Continental is very conscientious when it comes to pets after law suits a decade ago.The only alternative is a private charter flight in a small plane,there are many in Dallas/Ft.Worth area but very expensive.