Assume some rich nut sets up one of those giant Texas-sized ranches in Northern or Western Australia
Just to throw some 'do some research dust' in the works! Texas ain't nuthin!
From Wiki-
https://en.wikipedia.org/wiki/Anna_Creek_Station
'Anna Creek Station is the world's largest working cattle station.[1] It is located in the Australian state of South Australia. Its area is roughly 6,000,000 acres (24,000 km2; 9,400 sq mi) which is slightly larger than Israel. It is 1,977,000 acres (8,000 km2; 3,089 sq mi) larger than its nearest rival, Alexandria Station in the country's Northern Territory and over seven times the size of the United States' biggest ranch, King Ranch in Texas, which is 825,000 acres (3,340 km2; 1,289 sq mi). [2]'
And previously
https://en.wikipedia.org/wiki/Victoria_River_Downs_Station
Currently Victoria River Downs has an area of 8,900 square kilometres (3,436 sq mi) The property was once the world's largest pastoral property with an area of 41,000 square kilometres (15,830 sq mi), but following much of the land being resumed it is now less than half its former size, and less than half the size of the current largest, Anna Creek station.[3]
You left horses off your existing list and possibly dingos, along with a long list of birds