KING, Hertford, Early 19th century
You presumably have already found out that the IGI at familysearch lists 16 Charles King born/baptised in Hertfordshire within five years of 1823 - although admittedly there are some duplicates. There are another four on the British Vital Records Index. Statistically there may also be some non-conformist births which are not recorded.
At first sight the "best fit" appears to be a Charles George King, son of William and Ann King, baptised 23rd October 1825 at St John and All Saints, Hertford. Two sisters - Caroline (28th January 1821) and Harriett (8th June 1823) were baptised at the same church. However my first reaction was that it is not a good fit - and these doubts are confirmed when I checked the National Burial Index - to discover that a 21 year old Charles George King was buried at All Saints, Hertford in 1847.
Any further progress may well depend on further clues from Australia. In 1851 few agricultural labourers will have travelled more than half a days walk from where they were born - so going from Hertford to Plymouth would be a very significant journey. In fact I get the impression that few people who travelled voluntarily travelled alone. It is likely that a ship carried one or more groups of people who travelled together, starting from the same place in England and ending up in the same settlement in Australia. While it may not apply in this case, it is not that uncommon for someone who has emigrated to marry someone who came from the same English town or village and who travelled on the same boat. Your best bet might be to have a good look at the passenger list of the Caucasian to see who else travelled with Charles King - whether any others came from Hertfordshire - and if so what towns or villages.
It could also be worth checking whether Charles King is listed on the 1841 or 1851 census for Hertford. You should be able to get the microfilms at your local LDS Family History Centre - see familysearch for details (and there may be other genealogical libraries in Perth). Unfortunately Hertford was quite big, with a population of perhaps 6,000 which means there is a lot to check. There are indexes at HALS for Hertford for both dates - so you may prefer to contact them.
There is no obvious connection with the earlier inquiry KING, Hertford, 19th century.
If you can add to the information given above tell me.