In Australia, shipping and passenger records are generally held in the state the vessel arrived in.
You may like to vary your search to include archival resources in your area, as well as those in the family's port of arrival and country of origin.
Unfortunately the museum is unable to provide specific information about ships or arrivals.
Remember, searching for family history information takes time and sometimes records have been lost or damaged over time.
The Library has research guides that may help start your search.