I was just at SD Zoo 2 days ago and here is what I observed.
1) It's hot and sunny. The animals will be sleeping or hiding under shades and not easily seen. Thus, they are not easy to be shot no matter what lens you have.
2) About 1/2 of the animals on display are behind thick glasses. With the amount of reflections and glare, it is impossible to get good shots. I even tried circular polarizer filter, doesn't help
3) For everything else behind wires and cages, you will need 70-200.
I was shooting 5D3 and the longest lens I have is 24-70, which doesn't do any good. My wife was shooting a T2i with 24-105. She was able to get some good shots, but for some, it is still not quite long enough.
After a while shooting animals, you will get bored because they do not move much. The best bet is to put the focus on your kids, and only shoot animals that are interesting to see. After all, your kids will give you expressions. The animals will be just laying on the floors or branches, sleeping.