He was employed as Surgeon Superintendent on the emigrant ship Bussorah Merchant in 1837. The Bussorah Merchant arrived in Hobart on 12 December 1837 with male and female emigrants. 58 children and 4 adults died on the passage out from measles and small pox. The ship was sent into quarantine on arrival. 
Morgan Price married Harriet Louisa, daughter of Andrew Armstrong Esq., of Holycrossabbey, County Tyrone in Cork in September 1825. (Rev. Sir Francis Lynche Blosse, Bart). His wife gave birth to a son at Cove in 1832.
His eldest daughter Catherine Hatton Price married John H. Whitcroft, barrister-at-law on 22 October 1846 at Kirk Bradden, Isle of Man. 
He was on the List of Retired Navy Surgeons in 1841 
Morgan Price died at his residence, 14 Pembroke road, Dublin on 27 January 1860