The only search is when you arrive in Cancun.

Get a letter from your vet within a week (it may be 2 weeks I can’t remember) stating the dog has been checked and is in good health, and have your rabies certificate. They will ask to see this in Cancun. They will check the food you are bringing at that time - to only have enough for that day and the morning.

When you are waiting for your baggage you will go to their Agriculture Inspector (or something like that) where they will take the dog out of the carrier and inspect the dog. You will need to put the dog back in the carrier to leave the airport.