Only if the relationship bar is as full as it should be for best friends. Good friends and friends can become Old Friends, too. Best Friend status is based on the fullness of relationship bar, too.
Also - @lila - you can put pets up for adoption, yes. Pets aren't held to the same restrictions as Sims. The only thing that's the same for pets as it is Sims is life extending. No gourmet pet food and no young again potion for pets.