I bring my dog with me and if I was you I would listen to Cooper and not someone telling you to do something that they may or may not have got away with. More importantly will you? If you need more advice on this subject after contacting BAHA I'm sure you can get it here.
My pet has a Belize passport because we travel a few times a year. You need an import permit or a pet passport. You also need a Health Certificate and a Rabies Certificate. The Health certificate must be within 10 days of arrival if I remember correctly. If they tell you that your permit will be waiting for you at the airport you had better ask for a copy of the paperwork plus keep the email and bring all documents with you. It could get expensive for you if you don't. The cargo expense plus other fees about equals my airfare (my pet weighs 55#). No, on a round trip it is more than my airfare but I don't tell my wife that.
The loose advice that was given to you will not serve you well. To enter a foreign country for the first time and try to circumvent their laws is not something I would advise you to do. The last time I entered my pet's passport was suppose to be waiting our arrival. Guess what, it wasn't, but I had all the documentation and just waited them out after listening to extra fees because I didn't have the correct paperwork. They finally allowed me to pay the normal fee and my pet's passport was mailed to my destination.
Be advised that if your pet travels as cargo which most pets do, you will have to pay customs on the air cargo fare plus whatever fees are involved for inspection and permit. I insure you that it will be more than $50bz slipped to? The plus side is that Belize is a great place to bring your companion and you and your pet will love it because it can accompany you most anyplace you go. I'm assuming that your pet is well behaved. Good luck. (My dog likes to be with me but prefers to be with me in Belize than our home in the USA.) He didn't actually say this but I just know.