Was it's roof always corrugated iron?
Earliest photograph dated 1910 of Tranmere House
appears to show a corrugated iron roof.
I have found it interesting that most pre-1900's houses in Adelaide have corrugated iron roofs and I haven't seen a single period house of any style with a timber lined ceilings in the verandahs or portico areas (so you can see the roofing material whether it be corrugated iron or tiles).
I only know of one pre-1900's house in Adelaide with a slate roof, Dulwich House
Some research discovered "Australian Building: A Cultural Investigation
" by Miles Lewis which states that Adelaide had a timber shortage during the 1800's and early 1900's - the solution was to use corrugated iron sheeting for roofs enabling builders to reduce the conventional roof trussed structures required for the heavier roof tiles. This timber shortage also explains why verandahs and porticos weren't lined with timber as they are in Victoria.
According to Miles Lewis, the first corrugated iron stores in Australia were set up by Richard Walker of England (the original manufacturer of corrugated iron) in 1836 in Port Adelaide and Adelaide and most new houses today in Adelaide are still built with corrugated iron roofs.