Matthew Anderson was included in the Navy List of 1814. He was appointed to the Prometheus in 1815 
He was appointed surgeon superintendent on the Surry which departed 22 December 1818 and arrived in Port Jackson on 4th March 1819. He was granted permission to return to England on the Surry.
His next engagement was to the Mangles which left Falmouth on 11th April 1820 and arrived 7th August 1820. He returned to England and was engaged to act as surgeon-superintendent on the Mangles on the next voyage to Australia.
The Mangles departed Cork 21st June 1822 and arrived in Port Jackson on 8th November 1822. He returned to England on the Marshall Wellington in February 1823.
Castle Forbes 1824
His next voyage to Australia was on the Castle Forbes on 19th January 1824.
In all 681 convicts arrived in Australia under Matthew Anderson's care. In total he lost only six prisoners.
He was appointed Colonial Surgeon on 18 February 1824 and was granted land in 1826 which he called Redesdale. In about 1834-35 he had a weatherboard cottage built, with a separate stone kitchen to the rear. The estate was later called Manar. 
He was jury member at the inquest into the death of Lieut. Masters who died in the same accident as Lady Mary Fitz Roy in 1847 and was in charge of the Colonial Hospital at Parramatta for many years.
Matthew Anderson died at Parramatta on 7th July 1850 age 61 years. A neat marble memorial to his memory was placed in St. John's Church Parramatta in 1851. 
The late Dr. Anderson, who for so many years was connected with the useful and benevolent institutions of this town, has bequeathed the following sums:
To All Saints Church, in the parish of Marsfield 150 pounds; to St. John's Church, Camden 50 pounds; to St. John's Church Parramatta 20 pounds; to the Committee of the Water Works, for the purpose of erecting a fountain on the south side of the Parramatta River, 200 pounds; and to the District Hospital 300 pounds. As Dr. Anderson was officially connected with the hospital and Parramatta Bench for the last thirty years, during the whole of which period he conducted himself with much zeal and discretion in the public service, his name will long be gratefully remembered by the inhabitants of this town.
Notes and Links
1). Hambledon Cottage was built by John Macarthur in 1824 as a second house on his Elizabeth Farm Estate. Notable occupants in the early days included General Sir Edward Macarthur, Archdeacon Thomas Hobbes Scott and Dr. Matthew Anderson. The resident most associated with Hambledon is Penelope Lucas, former governess to Macarthur's daughters. It was she who named the family 'Cottage' after the township of Hambledon in Hampshire, England. - Hambledon Cottage at Sydney Architecture.
2). Matthew Anderson acted as private surgeon to the Macarthur family.