This information is not about your Gustaf Henrik Hvass, but the family name and birthplace sound like it might be of some interest to you?.
Applications for naturalisation from 1901 are matter for Australian government. From National Archives of Australian files -
application for naturalisastion in 1904 by Edward HVASS, cabinetmaker, 51 years old, born 17 April 1853, Aalborg, Denmark, arrived Sydney 28 Nov 1886 SS Hapsburg.
Married with wife, two sons and one daughter. He has lived all the time in New South Wales.
New South Wales Births, Deaths and Marriage online index
2615/1927 death Edward HVASS
father Jane P, mother Netta K GLEBE