The breeds and the requirements in trainer points to unlock them, credits to.

Unlockable	How to Unlock
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