It was a little red dot on a Zillow map. That was the first time Serena Dugan laid eyes on the Adirondack-style cottage, nestled into the quiet, coveted corner of Coecles Harbor on Shelter Island.

But in the remote West Australian town of Newman, another cat with attitude is helping those laying down the law, becoming something of a local online celebrity. The station, located about 1,170 ...