John Wilson Elliott was employed as Surgeon-Superintendent on four convict ship voyages to Australia:
Duke of Richmond to Van Diemen's Land in 1844
Marion to Van Diemen's Land in 1845
Joseph Somes to Port Phillip in 1847
Stately to Van Diemen's Land in 1849
Duke of Richmond 1843
The Duke of Richmond departed Dublin with 111 male convicts on 21 September 1843 and arrived in Van Diemen's Land on 2 January 1844. 
The Marion departed Woolwich 14 June 1845 with 301 male convicts and arrived in Hobart 16 September 1845.  John W. Elliot kept a Medical Journal from 18th May to 24th September 1845.
Joseph Somes 1847
The Joseph Somes with Exiles arrived in Sydney 23 October 1847. John W. Elliott kept a Medical Journal from 27 April 1847 to 8 October 1847
The Joseph Somes taken up by the Admiralty to convey male exiles to Hobart Town and Port Phillip fitted at Deptford and dropped down to Woolwich May 6th 1847 where she embarked her Guard and 165 male Exiles. On the 18th the ship quitted Woolwich for Cowes when she arrived on the 23rd of the same months and there 84 Parkhurst boys were received from Parkhurst Prison making a total of 249 then under my Superintendence. During the ships stay at Spithead several of the Parkhust Boys suffered from nausea and inability to take their food accompanied by more or less derangement of the bowels which ceased on going to sea. On the 4th June the ship sailed from Spithead, Wind at N.E
The Stately departed Woolwich with 169 female convicts arriving in Van Diemen's Land 2 September 1849.
In 1851 John Elliott resided with his wife Susan in Salisbury Street, Westminster. John was 43 and Susan was 30 years of age. He gave his occupation as Surgeon, Royal Navy (half pay) and place of birth Ireland. The couple lodged at the house of Thomas Richards, a builder.
Castle Ellen 1856
John Elliott was Surgeon Superintendent on the Castle Ellen convict ship to Bermuda. He kept a medical Journal from 9 November 1855 to 26 March 1856. 
Deputy Inspector of Hospitals and Fleets
He was promoted to Deputy Inspector of Hospitals and Fleets on 10 October 1865 and was on the retired list of 1867.
He is listed in the Medical Register 1865.
Date of Registration 1 January 1859 - Naval Hospital, Haulbowline, Queenstown, Ireland.
Member of Royal College of Surgeons England 1828
M.D. Univ. King's College Aberdeen 1856.
John Wilson Elliot died in September1887.....Probate of the Will of John Wilson Elliott, late of Grange in the County of Tyrone, Deputy Inspector-General Royal Navy, who died on or about 13 September 1887 at same place granted 8 June 188 at Dublin to Andrew Elliott of Omagh in the said county Solictor the brother one of the Executors.
 Ancestry.com. UK Royal Navy Medical Journals, 1817-1857 [database on-line]
 National Archives. Reference: ADM 101/254/1B Description: Medical journal of the Castle Ellen, convict ship from 9 November 1855 to 26 March 1856 by John Wilson Elliott, Surgeon Superintendent, during which time the said ship was employed in the conveying of convicts to Bermuda
 Ancestry.com. England and Wales, National Probate Calendar (Index of Wills and Administrations), 1858-1966, 1973-1995 [database on-line]. Provo, UT, USA: Ancestry.com