The Florentia was built at Newcastle UK in 1821. She brought prisoners to New South Wales from counties throughout England and Scotland in 1828 and 1830.
The Florentia got under weigh from Sheerness on the 18th August 1828 and proceeded across the Channel on 22nd. They put into Cork for fresh water on 1st September. Six prisoners were disembarked at Cork suffering from Typhus, among them Thomas Trigg, Matthew Bowen, James Brady and James Dempster.
The Florentia departed Cork on 15 September 1827.
The Military Guard consisted of a detachment of 29 men of the 40th regiment.
Passengers included Captain Barnett and wife. (This may have been Captain Barnett of the 40th who was severely injured at the Battle of Waterloo.)
Surgeon James Dickson
James Dickson kept a Medical Journal from 23 July 1827 to 14 January 1828 in which he kept a daily record of weather experienced during the voyage. The recordings commence on 11th August while the ship was moored at Sheerness. 
The wind was from the south-west when they arrived off Sydney on 3 January 1828. They came to anchor on the following day and entered Sydney Cove on 5th January under an easterly breeze.
A muster was held by Colonial Secretary Alexander McLeay on 5th January 1828. The indents include the name, age, education, religion, marital status, family, native place, trade, offence, when and where tried, sentence, prior convictions, physical description and where assigned on arrival. There is also occasional information regarding pardons, deaths and relatives in the colony.
The Monitor reported - On Monday last (14th), the prisoners who arrived on the ship Florentia were landed, when the usual inspection took place in the jail yard, previous to their distribution. They appeared very clean and healthy. We understand that ten of them, were immediately forwarded to Penal Settlements, pursuant to directions received from home they being troublesome or bad characters. We may draw an inference of the wretched state of England from the number of able young men who are continually arriving in this Colony. Upwards of one hundred of the prisoners by the Florentia, were under twenty one years of age !!'
The youngest prisoners on board may have been sent to the Carter's Barracks:
Joseph Acton (16)
Henry Beard (16)
William Castigane (16)
Alexander Donaldson (16)
Thomas Goate (16)
William Miller (16)
Thomas Westcott (16)
Richard Gadd (15)
William Hunt (15)
William Keith (15)
John Morin (15)
James Mills (15)
Patrick Ryan (15)
John Collins (14)
Charles Kinslow (14).
Four men were assigned directly to the Newcastle district. - Benjamin Cartwright, William Cooper, Francis Turner and Thomas Wright. They gave their occupations as miners and were probably assigned to work in the government run Newcastle Coal Mines.
Twenty three prisoners were assigned to the Australian Agricultural Company.. - Thomas Beckett, John Bond, Richard Barrett, Isaac Barnett, James Burnett, John Connor, Joseph Acton, Joshua Bowler, Henry Beard, John Baylin, William Bitton, John Culpin, William Castigane, John Clarke, John Crane, John Donaldson, Joseph Habberfield, Charles Kinslow, George Thomas, Charles Randall, Thomas Nicholls and James Stephen.
This was before the Company had control of the coal mines at Newcastle and so many of these men were probably assigned to work as shepherds in the Port Stephens district and north to the Liverpool Plains.
This was probably the case for Nathanial Burrows a potter from Derby, who to his great good fortune was also assigned to the A.A. Company on arrival. Burrows received his ticket of leave in 1832, and became a squatter holding a lease of 15,360 acres at Hanging Rock which had capacity of 500 head of cattle, and was known as 'the Hanging Rock Run'. In August 1851 while out on his run Nathanial Burrows spotted a stockman panning for gold along Swamp Creek. He rode to Tamworth to tell of his news and before long the rush to the Hanging Rock Gold Fields had begun.
4). National Archives - Reference: ADM 101/27/5 Description: Medical and surgical journal of the convict ship Florentia for 23 July 1827 to 14 January 1828 by James Dickson, Surgeon, during which time the said ship was employed on a passage to New South Wales.
 Ancestry.com. UK, Royal Navy Medical Journals, 1817-1857 Medical Journal of James Dickson on the voyage of the Florentia in 1828. The National Archives. Kew, Richmond, Surrey.
 Bateson, Charles Library of Australian History (1983). The convict ships, 1787-1868 (Australian ed). Library of Australian History, Sydney : pp.346-347, 385