The Mount Hotham airport is just 10km away from Dinner Plain (it’s actually closer to Dinner Plain than to Mount Hotham). The airport opened in 2000 and is Australia’s highest-altitude airport.
You can charter a personal flight to arrive at the Dinner Plain airport. The Mount Hotham website has a comprehensive list of the different charter services available. Prices can vary depending on the time of season, the amount of people going and the length of the trip. For example, a 12-seater from Tooradin Airport (outskirts of Melbourne) costs approximately $350 per person which includes all landing costs and petrol.
QantasLink have in past offered flights from Sydney to Mount Hotham airport. This service did not run during the 2014 season due to a predicted lack of demand (or since). It is not known whether the services will resume, but for further information you should enquire with Qantas Booking Information on 13 13 13. An alternative is to fly into Albury airport and then drive the 2.5 hour trip from there to Dinner Plain.
Some dog-friendly accommodation services offer a return transfer from the airport or you can hire a vehicle to transfer you.
