From PsyHelp

This page lists all the pet graphics available in-game and the pet's potential offspring. In March 2009 Ben changed the system; baby pets now have a father, and his graphic also influences the baby's graphics. This means that a list of potential offspring for each pet is now rendered obsolete.

Pets Commonly Available

These pets can be chosen upon sign-up, and are also available by breeding and items such as Scroll of Monster Summoning.

Pets Available Only Through Breeding

• These are available from Scrolls of Monster Summoning, too. May be available as new graphics when your pet is reincarnated.

Pets Available By Using Items In game