When people say there is a lot of driving between the two--they are not kidding. Even if you were lucky enough to have no traffic on the highways/roads between the two, you would be looking at a 1 hour drive from the zoo to the wild animal park. But of course you will hit traffic--and it will take longer. your 6 year old will be asleep the moment you leave the zoo and then you would be dragging the child through the wild animal park.

Seaworld--great option. Zoo--great option. Legoland--great option.
Wild Animal park--only a ok option. dont get me wrong, I love the place. but it is not off a major highway and is a pain to get to from anywhere.
If you are going to be driving from the OC area (since you will be at Disney) then your best and least painless option is Legoland. it means you will only have to drive to Carlsbad and that is about 20 miles closer than Seaworld or the Zoo. Legoland is right off the highway-and easy to get in and out of. you could keep your hotel in Orange county and do Legoland for the day.

--And its perfect for a 6 year old.

Have Fun!