We have always traveled with a dog, and that's since 1980. Now we travel with two, one Mexican.
Finally, for the first time, in October, we were asked for copies of a health certificate at the border in Lukeville/Sonoyita. They made a copy. That was it. Here's the link to the form, we fill it out on line, sign it, and print. http://www.petrelocation.com/pdf/APHIS7001.pdf
We are in a motorhome, and do not remove our pets (including a cat) if they choose to inspect us. We simply restrain them, and tell the inspectors that they are safe, and make sure that the dogs do not scare them. Both are large.
Have a great time, and enjoy having your pet with you! We provide "dog love" to people along the way who have flown in without their pets.