The Southern Whale Fishery Company was established in the Auckland Islands in 1850 -
The Auckland Islands, situated about 180 miles to the south of New Zealand, have been granted by the crown to Mr. Charles Enderby, and two of his brothers; and these gentlemen have placed them at the disposal of a company, which, on the 16th of January last, received a royal charter, incorporating them by the name of the 'Southern Whale Fishery Company.' Mr. Enderby intends to proceed forthwith to the scene of its future operations. The company propose to colonise these islands, as well as to carry on the whale fishery - Simmonds's Colonial Magazine and Foreign Miscellany
Charles Henry Hallett was employed as Medical Officer at the Auckland Islands. At the company annual meeting of directors and shareholders in 1851 he provided a Geological report on Enderby Island in which he described it to be invaluable for grazing and the cultivation of vegetables...... However, the cold, damp climate and acid soils made agriculture impossible, and the eight whaling ships attached to the station caught very few whales. Ultimately unsuccessful, the colony was abandoned in August 1852 
Charles Hallett departed the Auckland Islands before it was even abandoned. He sailed from on the barque Fancy on 16th January 1851 and arrived in Sydney on 1st February 1851. He was accompanied by his sister. The Empire in the shipping columns records the passengers on the Fancy as Dr. C. Hallett, Captain Brooks, John Taylor and Miss Hallett.
The next week Charles Hallett placed the following advertisement in the Sydney Morning Herald....
A Card - Mr. C. H. Hallett, Surgeon (late Chief Medical Officer to the Southern Whale Fishery Company at the Auckland Islands and formerly Demonstrator of Anatomy in the University of Edinburgh) may be consulted daily between the hours of ten and twelve am and two to four pm at Mrs. O'Reilly, Bridge Street, Sydney 
In a matter of a few short weeks he had moved to the Murrurundi district where he advertised his services.....
To Settlers, Shepherd and others on the Page. - Dr. C. H. Hallett (late Demonstrator of Anatomy in the University of Edinburgh) having purchased Dr. Welsh' s Practice begs leave to inform the Settlers and others in the Page district that he has fitted up a commodious hospital and that his charges for professional services will be on the most moderate scale, Murrurundi. 
Charles Hallett died on the 15th April, reportedly at the age of 26 -
Died - On the 15th April 1851, at Murrurundi, Charles Henry Hallett, Esq., M.R.C.S. London aged 26 years, eldest son of John Hallett Esq., M.R.C.S.I of Devonport England - late Demonstrator of Anatomy at the University of Edinburgh (4)
By May his belongings were being auctioned at his late premises. On offer was an extensive and varied assortment of the most valuable surgical instruments only recently imported on his orders as well as 54 volumes of rare medical works; drugs, chemicals and medicines; household furniture, horses and saddles.
Charles Henry Hallett is an enigma. There are several references to him employed as medical officer at the Auckland Islands station and sailing back to Sydney on the Fancy in 1851. He was in Sydney and Murrurundi briefly before he died, however information available about Charles Henry Hallett is inconsistent. That there was such a person as Charles Henry Hallett who was a Demonstrator of Anatomy at Edinburgh University there is no doubt. The several papers written by him and linked below confirm this, however Charles Henry Hallett who died in Murrurundi was only 26 years of age. Too young to have produced such work?
There was a Charles Henry Hallett who was born in 1826 in Middlesex who was the son of Timothy Hallett. Timothy Hallett was variously listed as an apothecary and surgeon (see below), however there are several others by the name of Charles Hallett who are listed in the 1841 census and may possibly be him as well. Two more possibilities are listed below.
Notes and Links
1). The Unlucky Enderby Settlement......The remoteness and small size of the settlement, and the long, dark winters the settlers had to endure, led to heavy drinking. Drunkenness, depression and family discord seems to have been a particular problem for the succession of Chief Medical Officers appointed to the islands. What happened to Dr Hallett on 14th October 1850? His sister tried to kill him. Apparently unable to cope with life with her brother, Miss Hallett discharged a shotgun at him, missing, reloaded and shot herself in the head. She sustained serious but not fatal injuries. Enderby decided to take no action against Miss Hallett after her brother promised there would be no further trouble. Hallett was dismissed two months later and brother and sister sailed for Sydney in January 1851. ........The Unlucky Enderby Settlement
5).An Account of the Anomalies of the muscular system, met with in the Dissecting room of the University during the years 1846 - 1847 with general Remarks. by C.H. Hallett, Surgeon, Demonstrator of Anatomy in the University of Edinburgh. - Edinburgh Medical and Surgical Journal
Census and other records: Charles Henry Hallett, son of Timothy (an apothecary) and Rebecca Hallett was christened at St. Matthew, Bethnal Green Middlesex on 7 September 1825. On the same day Sarah, daughter of Timothy and Rebecca was also christened. She was reported to have been born on 23 April 1823. (Ancestry.com. London, England, Births and Baptisms, 1813-1906 [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2010. Original data: Board of Guardian Records, 1834-1906 and Church of England Parish Registers, 1754-1906. London Metropolitan Archives, London
In the 1841 UK Census available at Ancestry, the family of Timothy Hallett were residing at No. 10 Mile End Low Town, Stepney, Middlesex. Timothy age 55 gave his occupation as surgeon. Rebecca was age 40. Sarah and Charles H. both gave their age as 15; Ambrose was 9 years old and Rebecca and Mary Harris were both one year old. Ancestry.com. 1841 England Census. Class: HO107; Piece: 713; Book: 7; Civil Parish: Stepney; County: Middlesex; Enumeration District: 22; Folio: 44; Page: 15; Line: 17; GSU roll: 438822.
In the 1841 UK Census there is a Charles Hallett age 25 who gives his occupation as surgeon and resides with Thomas Hallett age 70, Edward Hallett age 35, Robert Hallett age 30, Elizabeth Hallett age 40 and Jane Hallet and 30 at Axminster, Devon. .....Class: HO107; Piece: 200; Book: 5; Civil Parish: Axminster; County: Devon; Enumeration District: 1; Folio: 7; Page: 10; Line: 2; GSU roll: 241301. Ancestry.com. 1841 England Census
In the 1841 UK Census At Tiddells Court, Tiverton, Devon there is a John F. Quick listed as Surgeon residing with his wife and children as well as servants and a Charles Hallett age 15 who was a surgeon's assistant. Class: HO107; Piece: 255; Book: 10; Civil Parish: Tiverton; County: Devon; Enumeration District: 1; Folio: 16; Page: 26; Line: 12; GSU roll: 241325. Ancestry.com. 1841 England Census
 NSW Government. Inward passenger Lists. Series 13278, Reels 399-560, 2001-2122, 2751. State Records Authority of New South Wales. Ancestry.com. New South Wales, Australia, Unassisted Immigrant Passenger Lists, 1826-1922