Between 1825 and 1857, John Carmichael had worked non-stop in producing engravings, drawings, paintings and printings, as well as lithographs. To know certain number of his works cannot be achieved, however there is at least 13 known advertisement works John have done. Some are being shown below:
All images shown below can be found from State Library of NSW
And one of the three first Australian stamps in 1850:
And apparently he did several more stamps (1851, 1854, 1856 and 1860 (the 1860 stamps were re-produced from 1856 stamps)
The jury is still out there whether the whole stamp collection shown above are all works done by John Carmichael…
New South Wales was the first part of Australia to be settled by Europeans, and the first to operate a postal service, which in 1803 was carrying letters between Sydney and Parramatta for a 2d charge. In 1809 a collecting office in Sydneywas established to receive mail from passing ships, and in 1825 the postal service was expanded. Mail coach service began in 1830, and in 1835 a new Postage Act superseded the 1825 statute and set rates based on weight and distance travelled.
The postmaster of the time, James Raymond, was in communication with Rowland Hill in England and worked to encourage the prepayment of letters in NSW. In 1838, Raymond introduced envelopes embossed with the seal of the colony, and available for local mail for 1¼ pence each instead of the 2d charged letters paid for in cash. They are thus regarded as precursors of the Penny Black. However, the envelopes were not popular, and in 1841 Raymond was unable to develop official interest in postage stamps for the colony.
In 1842 regular mail service was carried by steamer between Melbourne and Sydney, and the first mail packet from Britain arrived in 1844. An act of 1848 reformed the postal system and authorized the use of stamps; the first stamps appeared on 1 January 1850. They were locally produced, and depicted a scene of Sydney and its harbour, thus becoming known as the “Sydney Views”. The 1d, 2d, and 3d stamps were separately engraved, and then re-engraved and retouched over the next year, yielding dozens of varieties.
In 1851 the colony switched to a more conventional design, a profile of Queen Victoria wearing a laurel wreath, first in a somewhat crude rendition, then a better one in 1853. The colony also took the unusual step of using paper watermarked with the denomination, a practice that resulted in a number of mismatches between watermark and printed denomination that are rare and highly prized today.
To view more stamps, see https://www.prestigephilately.com/auction168/haden_168.pdf and find some stamps in good conditions. And another site http://kennedystamps.com has a better list of stamps. It is quite hard to find better quality images of stamps John Carmichael did on the Internet, unfortunately.