Actually, you can adopt strays, adopt, and visit other sims and ask for a kitten/puppy.
Quote:
"Animal Rescuer
You have a soft spot for animals of all shapes and sizes. To see one being mistreated, abandoned, or neglected breaks your heart. That is why you've made it a personal mission to adopt as many pets as you can to help make their world a little brighter.
Lots of pets need to be adopted. Who will give them homes if you don't? Use the newspaper, computer, or phone to find animals that have been placed for adoption. Or maybe some of your friends are expecting a litter? Visit them and ask for a puppy, kitten, or foal."
Source:
The Sims 3 Pets Expansion Pack Prima Official Game Guide.
Author Asha Johnson. Prima Games; Random House, CA. 2011.