Hi,
On Google maps, it appears that the property in question is between South and Gold Streets, and may have been incorporated with adjoining parcels of land to form new business premises.
If you check with the "City of Fremantle", they may have taken further photograph's of said property prior to demolition for historical reasons.
http://www.fremantle.wa.gov.au/HomeAs Councils keep copies of all buildings plans, it might be possible to purchase the original drawing plans and build date of the home from them.
That would be a good in order to give you an idea of the size of the interior and exterior of home.
You can also check out Landgate in Midland and the staff there will perform a Historical search on that address, for the years that you want. That way you can establish exactly, the original owners, when it was occupied by your family and if it was demolished.
http://www.landgate.wa.gov.au/corporate.nsfTry a historical search from as early as possible to current date or 1 to 2 years after the last recorded time they lived there.
Unfortunately, you have to go into Landgate in Midland to perform Historical searches and costs about $19
Hope this help you in your search.
Kind regards
George