Oh yes, animals would defeat humanity hands-down.
Just look at the past: millions died through malaria, yellow fever, plague, etc. All these were spread through animal activity, such as rat fleas and mosquitoes.
Humans are still powerless against many diseases, i.e. the smallest organisms known to man. If such outbreaks were coordinated by all animals in the world, we wouldn't stand a chance.
Nice idea for FOX, alright; I don't know if they'd go for it, but I bet it would make an intriguing programme.