It is very easy to bring your pet to Mexico.   All that is needed is:
1. A vaccination certificate stating that your pet has been vaccinated against rabies, hepatitis, pip and leptospirosis.
2. An official health certificate that must be issued by a veterinarian no more than 72 hours before entering Mexico.

You may enter the country with up to two large pets (dogs or cats). If you want to enter the country with any more than two pets you would need permission, which could be obtained from the Mexican consulate nearest you. In any case, it would be a good idea to go to a Mexican consulate ahead of your trip and inform them of your plans. You will be relieved to know that there is no quarantine period required for bringing a pet into Mexico. You must note that airlines have certain restrictions on pet weight and pet size, as well as on pet containers. Furthermore, it would be a good idea to make travel plans well in advance. Before renting an apartment or a house, make sure you know whether pets are prohibited or not. Many apartments in Mexico either prohibit certain types of pets or set stringent restrictions on the size and weight of the pet – especially where dogs are concerned. Restrictions can also apply to cats, so make sure you sort out the details before signing a contract or a lease agreement.

Mexican Kennel Club
They have the contacts of dog breeders and trainers.
5655-1600

Asociacion Humana (Humane Society)
Animal shelter
5570-3433

Refugio Franciscan
Animal shelter
5570-0599

Anti-Rabies Center
5796-3770