Queensland birth marriage and death indexes are online and you can work out exact dates using the search boxes provided by gradually narrowing down your 'to' and 'from' dates.
https://www.qld.gov.au/law/births-deaths-marriages-and-divor...That page also has an "Information you can access" link which details the records that are closed to the general public
Queensland electoral rolls are available on Ancestry.
The marriage certificate for Anton and Rosina can be purchased from the UK GRO online and it will give the names of both their fathers and their occupations. You can then check this against the information on their death registrations to ensure it is correct.
It doesn't look like any of the children who arrived with them were born in the UK so were probably born in Switzerland.
Anton's Australian naturalisation record is digitised at the National Archives:
http://soda.naa.gov.au/record/34415/1