In Nintendogs + Cats: Toy Poodle and New Friends for the Nintendo 3DS, there are quite a few breeds you can unlock with trainer points. Here is the list of breeds you can unlock, and how many trainer points you need in order to unlock them.
Basset Hound – 3600
Beagle – 3600
Cavalier King Charles – 2000
Chihuahua – 5800
Cocker Spaniel – 3600
Dalmatian – 7400
Daschund – 5800
German Shepherd – 7400
Great Dane – 600
Husky – 2000
Maltese – 2000
Mini Pinscher – 7400
Pug – 600
Shetland – 5800
Yorkshire – 600