Edward Caldwell was born in Ireland in c. 1790. He was included in the Navy List of Medical Officers in 1814.
At Millbrook, Southampton in 1817 Edward Caldwell of Redbridge married Mary Ann Terill of Lyndhurst.
Mary Anne Caldwell died at La Raite (?Demerara) in 1841  - Caldwell, Mary Anne, wife of Edward Caldwell, Esq. Surgeon R.N. lately at La Retraite
Edward Caldwell was appointed to H.M.S. Cambridge in the Mediterranean on 6 February 1840. H.M.S. Cambridge was built in 1817 and was of 2139 tons. 445 officers and men, 60 boys and 150 marines were on board. Edward Barnard was Captain and J.P. Parkin Commander. Edward Groves and Walter W. Lennox were employed as Assistant Surgeons. 
Edward Caldwell was appointed Surgeon Superintendent on the convict ship East London in 1843. He kept a medical journal from 13th April 1843 to 28th September 1843.
The East London arrived in Van Diemen's Land from Dublin on 21 September 1843. An astonishing nineteen women and twelve children died on the voyage out. This was the most deaths that ever occurred on a female convict ship to Australia. 
Edward Caldwell sailed from Hobart to Sydney on the Lord Petrie in November 1843 and returned to England on the Ocean in February 1844 
In 1847 he was appointed to the Ceylon at Malta. 
In the 1861 Census Edward Caldwell, age 71, widower and retired surgeon of Royal Navy, is recorded as living at the residence of his son Charles and his wife Sarah Caldwell and son Edward age 4. Charles Caldwell who was born c. 1824 at Millbrook, Southampton was incumbent at St. Martin's at Oak, Norwich.
Edward Caldwell died on 1st May 1863 aged 74. His Memorial at St. Martin's at Oak, Norwich states: Sacred to the memory of Edward Caldwell Esq. Surgeon R N. The deceased was for more than fifty years An officer in his majesty's service and received Two medals for distinguished service in Syria and Algiers.
3). The following notice published in the London Gazette in 1835 may be related to Edward Caldwell:
Notice is hereby given, that the Partnership heretofore subsisting between us the undersigned Edward Caldwell and Edward Sabben, both of Millbrook, in the County of Southampton, Surgeons, Apothecaries and Men Midwives, was dissolved on the 31st day of December last. All debts due and owing to and from the said Partnership will be paid and received by the said Edward Caldwell. 31 July 1835.
4). National Archives. Reference: ADM 101/22/1 Description: Medical journal of the East London, convict ship from 13 April to 28 September 1843 by Edward Caldwell, Surgeon Superintendent, during which time the said ship was employed in her passage from Dublin to Hobart Town, Van Diemen’s Land.