The Prince Regent was built at Rochester in 1811. This was her first voyage bringing convicts to Australia.
Surgeon Alexander Taylor
Alexander Taylor kept a Medical Journal from 21 June 1820 to 17 January 1821. He joined the Prince Regent on 21 June 1820 at Deptford and sailed to Cork to embark the prisoners. 
On the 13th July 1820 a detachment of the 1st Royal Scots under orders of Lieut. Lewis formed the guard.
The prisoners' names and details were recorded according to the county they were convicted in and include name, age, date and place of trial; offence and sentence. Offences committed included stealing wheat, pig stealing, sheep stealing, street, robbery, house robbery, conspiracy to murder, picking pockets, vagrancy, highway robbery, larceny, abduction and having forged bank notes.
On 20th August 1820, twenty-eight convicts who were transferred from Dublin to Cork on the brig Atlas were received on board. The following day another 104 convicts were received from the Cork depot. Another five were received on 25-31 August. In total 144 prisoners were embarked. 
An order for transportation dated 12th September 1820 can be found in the Colonial Secretary's Papers -
By the Lord Lieutenant General and General Governor of Ireland...Whereas the several persons named in the annexed list have been convicted of offences against the laws of Ireland and have been ordered to be transported for the terms annexed to their names respectively; and whereas the said several persons have been put on board the ship Prince Regent in order to their being transported to His Majesty's Colony of New South Wales, we do hereby in pursuance of the authority visited in us by Law transfer the indices of the several persons so convicted to His Majesty's Governor of His Majesty's said Colony of New South Wales, and assigned for the terms for which they have been respectively ordered to be transported. Given at His Majesty's Castle of Dublin the 12th day of September 1820. 
The Prince Regent weighed anchor at 5am on 19 September 1820.
Trinidad was sighted on the 3rd November 1820. 
There was some fighting amongst prisoners on the voyage out. Alexander Taylor punished the offenders by putting them in handcuffs. Several men were also insolent and critical of the rations that were provided however there is no mention of any harsher punishments.
Alexander Taylor delivered all 144 prisoners in a healthy state when the vessel arrived in Sydney on 9 January 1821. The voyage had taken 112 days.
On Monday 15th January the prisoners were mustered and inspected by the Colonial Secretary and on Tuesday 16th January, the prisoners were all up and had a complete suit of clothing issued to each of them by an Officer from the Deputy Commissary General Department. On the 17th the men were disembarked early in the morning. They were inspected by Governor Macquarie at 10am.
Departure from the Colony
The Prince Regent, Captain Clifford, was preparing to leave the colony in February 1821. Chief Officer Mr. Murdock and Second Officer Mr. Allen.
 Bateson, Charles, Library of Australian History (1983). The convict ships, 1787-1868 (Australian ed). Library of Australian History, Sydney : pp.344-345, 383
 Ancestry.com. UK, Royal Navy Medical Journals, 1817-1857. Medical Journal of Alexander Taylor on the voyage of the Prince Regent in 1821. The National Archives. Kew, Richmond, Surrey.
 National Archives - Reference: ADM 101/61/1B. Medical and surgical journal of the ship Prince Regent for 21 June 1820 to17 January. Medical and surgical journal of the ship Prince Regent for 21 June 1820 to17 January 1821 by Alexander Taylor, Surgeon Superintendent, during which time the said ship was employed in a voyage from Cork to New South Wales. The journal takes the form of a diary recording the daily routine of allowing prisoners on deck in divisions, cleaning and ventilating the prison and hospital, casks opened, windsails up, prayers and wine issued. No individual cases are recorded and the abstract and general remarks record no disease or accidents, some slight colds are mentioned in the diary.