Robert Malcolm was appointed Assistant Surgeon in the Royal Navy on 10 June 1812.
In 1816 Robert Malcolm was appointed supernumerary assistant-surgeon to St. Helena . This appointment was to HMS Conqueror, flag ship of Rear-admiral Robert Plampin.
Admiral Sir Pultenay Malcolm was commander-in-chief at St. Helena at this time.
Robert Malcolm was appointed Surgeon, Royal Navy, in September 1819.
He was appointed Surgeon Superintendent on two convict ship voyages to Australia:
1). Sovereign to Van Diemen's Land in 1827. The Sovereign under Captain Mackeller departed London 22nd July 1827 and arrived 19th November with 81 female prisoners. Passengers included Rev. W. Yate and Missionaries Mr. and Mrs. Butler, John Abbott and Peter Ogilvie.
Robert Malcolm married in 1831.......Marriage - At Camberwell, Robert Malcolm Esq., Surgeon, Royal Navy to Caroline, widow of James Wilkinson, Esq., late of Malta. 
Surrey County Gaol
He was appointed to Surrey County Gaol in the Easter Session 1835. Salary £150 per annum. 
Moore Place Lambeth
Robert Malcolm age 45
Caroline Malcolm age 45
Ellen Wilkinson age 25
Henry Wilkinson age 25
James Wilkinson age 20
Alfred Wilkinson age 15
Adelaide Wilkinson age 15
Robert Malcolm died at Moore Place, Lambeth in October 1842 aged 45.
Camberwell - Mr. Robert Malcolm, whose recent death has caused a vacancy in the office of surgeon to the Surrey county gaol, has bequeathed the sum of £1000 to be paid at the demise of his wife, to the Royal Naval School at Camberwell, to found a scholarship or exhibition to be entitled the Malcolm Exhibition. Mr. Malcolm, who was a surgeon in the Navy, was one of the council of the school. 
Royal Naval School at New Cross. Founded in 1843, the school was a charitable institution for the sons of Royal Navy officers. The school moved to Chiselhurst in 1899, and the buildings now form part of Goldsmiths College - National Maritime Museum
The Royal Naval School was a charitable institution founded in 1831 to provide an education for the sons of naval and military officers in needy circumstances, with a preference for orphans of those killed on active service. The school opened in temporary premises in Camberwell in 1833 and moved to its purpose-built premises in New Cross in 1844. 
Will of Robert Malcolm
I direct all my just debts, funeral and testamentary expenses to be paid as soon as may be after my death. I desire to be buried with the respect due to my station at the Cemetery at Norwood. I give to my dear wife Caroline the sum of one hundred pounds and also all my books, plate, wine, furniture, carriages and other effects of a similar nature absolutely.
He also made generous bequests to his wife's children by her first marriage, to his friends, to servants (the sum of a year's wages), to his God daughter and to his cousin in Edinburgh as well as the £1000 for the Naval College scholarship. The residual of his estate was to be held for his wife. 
In 1857 his bequest on the death of his wife of £1000 to the Naval School to found a university scholarship, was announced.