Firstly, there's nothing such as 'Her Majesty's Victorian Ship'!
There WAS a such as H.M.V.S. as a ship prefix- as observed by this ship's preservation website.
http://www.cerberus.com.au/
Her Majesty's Victorian Ship was the official title of a ship in the Victorian Navy. In this case, 'Victorian' does NOT refer to the Queen of England, it instead refers to the Australian territory named after her. There was also H.M.Q.S. (Her Majesty's Queensland Ship) used prior to the federation of the Australian territories.
While the ship was paid for by the Admiralty (80%), it was given to the Victorian government for defense of the coast, if it was to do anything else, it came back under Admiralty orders. In it's service life it barely ever left Port Phillip bay, so it never was under the Admiralty. Not sure though....?
As far as the sources I have (Conways, many websites) the vessel was strictly in service with the Her Majesty's Victorian Navy. You're right in that it was very static- it only left Port Philip Bay for gunnery practice as far as I can find. So,
H.M.S. would actually be incorrect for this ship.
Closest thing I can compare this to is a U.S. National Guard Unit- while we are part of the 'Big Army' in wartime, we are always listed as "XXXth
UNIT NAME,
HOME STATE National Guard."