Puppies are a newer It Girl feature. It allows you to find and keep a puppy.
At the moment, there are 3 breeds of puppies available. You get a puppy by petting a dog you like. It will then ask you whether you would like to be its owner. If you agree, you will have to wait to adopt it for maximum 1-3 days. Then, the dog is yours.
You can get a puppy anywhere: either on the street, in stores or at parties.
However, besides all the fun you can do with your puppy, they do not give any energy or confidence bonuses back. Besides that, if one is not careful, you can lose your puppy easily.