Kevin & Kell/WMG

The human world and Domain are in a Stable Time Loop.
The two worlds run parallel to each other. So when the birds discover time machines and go back in time to avert their Crapsack World, so do the humans of the future to avoid their Crapsack World. And the worlds in the past they go to are actually each other's worlds. So in what was formerly Domain, humans started to populate the earth, and in what was formerly the human world, animals start to populate the earth. We've already seen what caused the human world to go crapsack and the birds to find the time machine in canon. What caused Domain to go to hell was

In other words...

When Ray used the intelligence ray on himself, he kept some of the intelligence he gained
Although it can be explained with Characterization Marches On, Ray started out as a ditz who couldn't identify his natural enemies. While he realized that being as much of a genius as he was would potentially attract Lindesfarne to him, he decided against making himself as stupid as Pat Buchanan. After reverting back, he doesn't have any brilliant moments, but he doesn't do anything especially stupid, either, and seems more insightful about certain aspects of himself (like the changing nature of his relationship with Tammy).

The former human world is 'Earth-That-Was' from Firefly.
Think about it. The folks from the Firefly 'verse left the world when it was too polluted to sustain their numbers. What did the birds say their former world was like, and what happened to their humans? (Note: this isn't Domain's planet, but the original bird homeworld.)

The Bird's plan was doomed from the start
There's no reason why intelligent animals would be better than humans. Real animals regularly destroy their environments when population control factors (predators, competitors, parasites) disappear.
 * Just like Danielle pointed out.

In a portal imbalance, humans actually gain instincts.
To be more precise, they take on animal instincts not of their own. This leads to an uprise in the furry fandom. After all, all those lost instincts have to go somewhere.

More humans will come to Domain.
This troper thinks that Holbrook will introduce more humans at some point...and hopefully we'll see the first human villains in this comic.

Rudy's portrayal of humans was more accurate than it appeared.
Life is extremely adaptable and while humans created tons of evolution and might even be the next metior if we create a landscape of nothing but nuclear waste and styrofoam life will adapt to feed off of nueclear waste and garbage. If humans actually destroyed the world it would have had to be partly intentional.

There will be overpopulation of rabbits in the future
Since Kell is married to Kevin and is now the CEO of Herd Thiners, Herd Thinners employees no longer hunt rabbits in fear of getting fired. This will lead in to overpopulation of rabbits in the future and Kell will need to step down so that predators can hunt rabbits without fear, thus returning them to stable numbers.