My Sim moved to a house that happened to have a dog house and my two cats tried for kitten in the dog house.
@Simstar:
With a high relationship bar and some friendly interactions, romantic interactions will become available. From there, you choose Try for Puppy (or Kitten or Foal). They will go to the dog house or stable. I heard the chimes when they were done, so I guess that part is the same as with Sims. I don't know yet if my cat is pregnant, but she probably is.