William Rogers M.D., was appointed Surgeon in the Royal Navy in 1814 
He was appointed Surgeon to H.M.S. Firefly Steam Vessel at Falmouth on 20 December 1833. 
Surgeon Superintendent convict Ships
He was employed as Surgeon Superintendent on two convict ship voyages to Australia:
1). Arab to VDL in 1836.
2). Richard Webb to VDL in 1842.
Convict Ship Arab 1836
The Arab arrived in Hobart from London on 30 December 1836 with 131 female convicts
...Signature of William Rogers in the Medical Journal of the Arab.
Emigrant Ship Layton 1838
It is probably the same William Rogers as above who was employed as Surgeon Superintendent on the emigrant ship Layton in 1838. The Layton departed from Bristol in September 1837 and arrived in Sydney in January 1838. Cabin Passengers included Rev. Mr. Rogers and Mrs. Rogers. On the document of arrival it was stated that there were 122 emigrants and 110 children. Two crew members died and seventy children on the passage out. Measles had broken out soon after leaving the Channel. He was on the List of Surgeons remunerated for services as Surgeon Superintendents, being paid £200 for his services on the Layton. Passenger list of the Layton
Quarantine Station 1838
In February 1838 Dr. Rogers took the place of Dr. Gavin Browning at the Quarantine station where the passengers who arrived on the fever ship Minerva were being cared for.
He took up residence in Ward No. 1, a portion of which was partitioned off for his use.
A. A. Company 1838
It may be the same William Rogers who was employed by the A.A. Company at Tamworth 
Convict Ship Richard Webb 1842
The Richard Webb departed Dublin 5th November with 199 male prisoners and arrived in Hobart on 4th March 1842. Four women, six children, five free settlers and six children of prisoners also came on the Richard Webb. William Rogers kept a Medical Journal from 15 October 1841 to 9th March 1842. He departed for London again on the Fanny on 17 June 1842.
Signature of William Rogers on the Medical Journal of the Richard Webb