This is an interesting challenge, for it can go from the impossible to the very easy.
The impossible would be trying to make empires and states encompassing the almost universal range of animals like the Grey Wolf, Orca/Killer Whale, Peregrine Falcon, Rock Pigeon.
But then the easy would be creating states (well the challenge is Empire so I do not know if they would qualify) that encompass the range of highly specialized, unique, rare, often endangered species. Examples would be the Indian Lion, Giant Panda, Galapagos Tortoise, Javan Rhino (which all today have their wild populations encompassed within one single state, and historically an empire).
For middle of the road options though, meaning animals which have larger ranges but nothing universal, I'd put forth the "Dominion of the South" or "Empire of Southern Pole", basically an empire consisting of: The Galapagos, coast of South America from Ecuador to Tierra del Fuego and up till Rio de Plata, South Africa and Namibia, Australia, New Zealand, Antarctica, and the plethora of isles and islets that dot the Southern Seas. This should firmly put ALL species of penguins under the same flag.