I'm not all that amazed that Webster 1913 doesn't have this definition; "station" in Australian English also means, simply, "large farm" or "ranch"
- Ban Ban Springs Station is about 200 miles from Darwin.
- Do you know when Mount Ringwood Station will come in for their mail?
- How long you been jackaroo on cattle stations?
In the second example, the typical rural English trick of applying the property name to the people who live there is being used. In the third example, the grammar is incorrect, but accurate.
This usage probably comes about as a conflation of the 3(b), 3 (c), and 4 definitions below, as well as the radio meaning above. As most large farms in Australia are extremely remote, in times gone past their only method of contact with the outside world was by shortwave radio. Yes, they didn't have phones; yes, this was still true as recently as the late 1970s.
NOTE: Since the re-input of the Webster 1913 text, this definition has been added! Which shows, if nothing else, that "station" being used in this sense is quite probably more than 100 years old.