I agree with everyone else. The Zoo alone could fill two days with a six year old, but the Wild Animal Park is a fantastic destination.
When are you visiting? The Zoo enjoys San Diego's typically Mediterranean weather while the Wild Animal Park shares its climate with Southern California deserts. Not unlike the Australian Outback. Think very hot. In the summer and fall, temperatures at the Park can exceed 100F, making long walks there very uncomfortable, unless your six year old is a very hearty soul.
We're members of the Zoo and Park, and tend to visit the Park more in the winter and early spring, visiting the Zoo more in the summer and fall.