It is possible to see William on the QLD Electoral Rolls and in order to register, he would of course, have to be a naturalised citizen.
http://www.archives.qld.gov.au/Researchers/Indexes/Courts/Pages/Naturalisations.aspxPerhaps this is him listed twice in the index
RATHE William
number 29
Year 1899
Ref. 1697781 A/49120 Z1998
RATHE William R
Number 29
Page 112
Year 1899
Ref 841184 SCT/CF38 Z2287
The other of the surname may be related (also listed twice

)
RATHE George
Number 12
Year 1896
Ref 1697781 A/49120 Z1998
RATHE George R
Number 12
Page 55
Year 1896
Ref 841184 SCT/CF38 Z2287
George is listed on the QLD 1903 Electoral Roll as a butcher in Rockhampton at Weinbolt Street.
No others of the surname with him