In Nintendogs + Cats: French Bulldog 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.
Beagle – 3,600
Boxer – 3,600
Bull Terrier – 600
Cocker – 2,100
Corgi – 2,100
Dachshund – 600
Golden Retriever – 9,800
Great Dane – 7,400
Jack Russell – 7,400
Labrador – 5,800
Maltese – 3,600
Mini Pinscher – 2,100
Miniature Poodle – 9,800
Pomeranian – 5,800
Pug – 7,400
Schnauzer – 5,800
Shiba Inu – 9,800
Shi-tzu – 600