I always thought the Old Dart might have been a reference to Dartmoor since there were a lot of convicts sent to Australia, but on reflection there might not have been a prison on Dartmoor in those days. Maybe someone more genned up than me would know.
It's been suggested that 'Dart' is a corruption of 'Dirt', and the 'Old Dirt' meant England.. Seems gold-diggers in Australia used to refer to gold-bearing soil as 'Dart'.