Joseph Cook was included in the Navy List of Medical Officers in 1814. He was appointed Surgeon to the Leven in 1818
He was employed as Surgeon Superintendent on seven convict ships to Australia :
Southworth departed Cork 18 November 1821 and arrived in NSW on 9 March 1822. Intending to depart on the Southworth for England later in March.
Sir Charles Forbes departed Portsmouth 25 January 1825 and arrived in Van Diemen's Land 18 April 1825. 128 male convicts arrived on the Sir Charles Forbes, two having died on the voyage. Dr. Cook departed from Sydney on the Deveron on 25th May 1825
Phoenix departed Dublin 27 August 1826 and arrived in NSW 25 December 1826
Louisa departed Woolwich 24 August 1827 and arrived in NSW 3 December 1827.
Mellish departed Falmouth 2 January 1829 and arrived in NSW 18 April 1829. He departed for London on the Harmony on 23 October 1829
Forth (11) departed Cork 3 June 1830 and arrived NSW 12 October 1830
Portland departed Portsmouth 22 November 1831 and arrived in NSW 26 March 1832. He returned to England on the Portland in June 1832.
Joseph Cook married Jean McDonald at Kirkaldy in 1834