You can hear a recording of the McNulty Family singing FAR AWAY IN AUSTRALIA at The Internet Archive; it is item #18 on the menu on that page. The recording is apparently from Decca (USA) 12256 made 11-Jun-1942.

The British Library and the State Library of Queensland have sheet music described thus:

FAR AWAY IN AUSTRALIA
Words by Charles Wilmott; music by Hermann E. Darewski
London: Francis, Day & Hunter, ©1908.