James Osborne was born in Dromore, Co. Tyrone, Ireland. He may have been a cousin of Naval Surgeons Alick Osborne and John Osborne who both settled in Australia.
There were two Royal Navy surgeons by the name of James Osborne in the relevant years:
James Osborne Date of Appointment Royal Navy 22 May 1811
James Osborne Date of Appointment Royal Navy 2 October 1813
He married Miss Mary Clarke, daughter of William Clarke Esq., of Lifford Co. Donegal in 1815 - Strabane Morning Post November 21, 1815 
APPOINTED TO THE AURORA
James Osborne was surgeon on the Aurora in 1827
James Osborne was employed as Surgeon Superintendent on four convict ship voyages to Australia:
James Osborne was appointed Surgeon to H.M.S. Camperdown Flag ship at Sheerness in 1842 
He was appointed to the Poictiers in 1843
MARIA SOMES IN 1844
In 1844 James Osborne was appointed Surgeon Superintendent on the Maria Somes. The Maria Somes arrived in Van Diemen's Land from London on 30 July 1844. After off loading the convicts she continued to Sydney with passengers Rev. Dr. Willson, Rev. James Cotham, Dr. Wilson, Captain Larkins, Lieut. Waldegrave, Ensign Welch and Surgeon James Osborne.
While in Sydney James Osborne made the acquaintance of David Burn who had arrived in Sydney from Tasmania on the ship London, J.T. Atwood, captain, on 31 July 1844. Burn kept a journal in which he described his stay in Sydney in detail, commenting on its social life, personalities, buildings, scenery and shipping. He mentions James Osborne on several occasions:
Wednesday 4th September - Dr. James Osborne R.N. has come here to reside. His ship, Maria Somes, sailed this day with the remainder of the 80th Regt.
Friday: 6th September - Missed Dr. Inches at breakfast, his yesterday’s society so pleasant as to induce his remaining all night; Dr. James Osborne, one of the most pleasant, merry fellow, far more of the Jolly Jack Tar than the Medico - took his brother officer to task in his own facetious way. In parliamentary phrase, Inches explained, giving a good account of himself. In countenance Osborne is a close resemblance to the Hibernian Oracle, but entertains no such sympathy in disposition.
Friday: 11th October: I was greatly grieved to hear by letter Inches received that Dr. James Osborne had a fall from his horse and hurt his hip. He is a right good fellow, and a jovial seaman of the true British breed. I trust he may be quickly restored to himself and his friends........
David Burn sailed to Port Macquarie, Newcastle and the Hunter River in September 1844. Select here to read Excerpts from his Journal describing his voyage on the steamer and his visit to the townships of Newcastle, Morpeth and Maitland in 1844. He also sailed to Norfolk Island on the Agincourt in December 1844.