The Brilliant referred to was certainly a merchant vessel, not naval.
1834 Lloyds Register records the Brilliant, A G Hopton commander, 196 tons, built in Sweden, 1804
rigged as a ship, sheathed with copper, single deck, built of oak and fir as sailing to Van Diemens Land in 1833-34. The description is later amended to being rigged as a Brig, which coincides with newspaper reports
From The Public Ledger and Daily Advertiser, 16 February 1831:
“Is entered Out at the Custom House, and will Sail in all this Month, having a great part of her Cargo engaged:
For HOBART TOWN, VAN DIEMANS LAND
the fine coppered Ship BRILLIANT;
Abney George Hopton, Commander; burthen 250 tons; lying in the St Katherine Dock.
Has very superior accommodation for Passengers, having 6 feet 6 inches between decks
and will carry an experienced Surgeon
For Freight and Passengers, apply to:
BUCKLE, BAGSTER and BUCKLE, 33 Mark Lane”
Abney George Hopton, was shown as the captain of the ship Mary Ann that sailed from Plymouth for New South Wales in May 1829 before being shown in command of the Brilliant; his will was proved in 1841.
Searching ship movements in Lloyds List for the period, shows the Brilliant, Hopson, on at least two round trips to Australia:
27 May 1831 sailed Plymouth “for Van Diemens Land”
reported arriving Hobart 15 November with cargo and passengers; later to Launceston and Sydney. Sailed in April 1832 to return to England loaded with sperm oil and wool
10 May 1833 sailed Deal for Cape of Good Hope and Australia
8 November – arr Swan River. A very full report of the cargo carried is listed in the Sydney Herald 17 February 1834. Also noted two passengers – Mr P C Abbott and Mrs Soder and child
8 Dec 1833 – reported departing Swan River, for King Georges Sound and Hobart
25 Jan 1834 – reported arriving Hobart “from King Georges Sound”, with cargo and passengers, Mr Jordan, Mr O’Neil and Mr Lewis
10 Oct 1834 - arr Gravesend from Sydney NSW