In Nintendogs + Cats: Golden Retriever 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 – 9,800
Boxer – 5,800
Bull Terrier – 3,600
Cavalier King Charles – 5,800
Chihuahua – 600
Corgi – 7,400
Dalmatian – 3,600
French Bulldog – 9,800
German Shepherd – 2,100
Husky – 5,800
Jack Russell – 600
Labrador – 3,600
Miniature Poodle – 9,800
Pomeranian – 2,200
Schnauzer – 2,100
Shetland – 600
Shi-tzu – 7,400
Yorkshire – 7,400