Don't take the 30-days requirement too seriously. Border officials everywhere live and die by bureaucratic paperwork.
Prepare a dossier on the pooch using a manila folder. Inside, have color images pages of the animal (which won't hurt if it gets lost).
The vet's forms. And an image of the dog's USA collar rabies inoculation (dog) tag.
When it comes time, the official will ask for the form, give a big smile and hand over the manila folder.
So far this has worked incredibly well, even with an official by the name of Hector at La Mesilla, who is notorious with dog hassles (he is said to hate them).
Good luck and please report your own experience,