Hi Eveder
The Victorian death certificates are very informative. Youcould purchase a certificate on line and download immediately for AUD$17.50.
http://online.justice.vic.gov.au/servlet/bdm_homeThe time in Australia is noted on the death certificate - if the informant had the information. You will need the Registration No and Year of death -
Death
SMITH John Peter
Father Smith Job Mother Elizabeth EAGLE
Age 68
Death Place South Yarra Year 1900 Reg. No 7145
You could search on
http://proarchives.imagineering.com.au/index_search.asp?searchid=23for Unassisted Emigrants or
http://proarchives.imagineering.com.au/index_search.asp?searchid=24for Assisted Emigrants
but identifying your John SMITH on the index may prove a bit difficult

I also found the following
MarriageSMITH John Peter = BEATTIE Emma
1862 Reg No 2264
BirthsSMITH John Edward
Father John Peter Mother Emma BEATTIE
Birth Place MELBOURNE Year: 1861 Reg No 12348
SMITH Florence Mary
Father John Peter Mother Emma BEATTIE
Birth Place Prahran Year1863 Reg No 3652
SMITH William
Father John Peter Mother Emma BEATTIE
Birth Place Prahran Year 1864 Reg No 24126
SMITH George
Father John Peter Mother Emma BEATTIE
Birth Place Prahran Year 1866 Reg No 23429
SMITH Charles Henry
Father John Peter Mother Emma BEATTIE
Birth Place Prahran Year 1868 Reg No 4780
SMITH Thomas Frederick
Father John Peter MotherEmma BEATTIE
Birth Place Prahran Year 1869 Reg No 17953
SMITH Edward
Father John Peter Mother Emma BEATTIE
Birth Place Prahran Year 1872 Reg No 4725
SMITH Francis Bertram
Father John Peter Mother Emma BEATTIE
Birth Place Prahran Year 1873 Reg No 19132
Cheers
cando