Hi Dinmalek and Sillylupie,
Actually there is already such a section in our main PetFinder system, although it isn't prominently displayed as we are giving emphasis to pets seeking adoption.
All you need to do is login to your PetFinder account, then proceed to create a pet profile and mark its status as Owner's Pet. If you wish to list other owner's pets, you can go to the search bar at the top of the page, select "Owner's Pet" and click Find Now. You can also refine the search to particular types of animals or breeds.
Anyway, thanks for the suggestion, I'll look into further improving the section