The Permanent Naval Forces came into effective existence in Victoria in 1867 with the acquisition of HMVS Nelson, an obsolete, Napoleonic era line-of-battleship. More vessels were added later. Permanent Naval Forces personnel were usually supplemented by members of the Naval Brigade. They were paid professionals.
In terms of the ownership of the Permanent Naval Forces, the article 'Naval Force of the Australian Coast' (Argus, Friday 13 May 1859, p.4) quotes a debate on the 'state of the naval force on the Australian coast' originally printed in The Times.
'The present force consisted of three or four small vessels, which were a detachment from the forces at the Indian and Chinese stations. ... During the late war [Indian Mutiny?] the senior officer at the Australian station expressed his surprise in the strongest possible terms that colonies so important as the Australian should be protected by so miserable a force.'
'He thought the mother-country ought to afford facilities to the colonies to form a separate naval force if they chose, and to give them sufficient protection till they had done so. He believed the Australian colonies were ready to form a naval militia for their own defence'.
This was published the same year as the Naval Brigade was formed, so perhaps some action was taken on this officer's suggestion.
National Archives of Australia Fact Sheet 134: 'Colonial defence personnel records held in Melbourne'
Argus, Friday 13 May 1859