It is likely that the infant John Bunham mentioned in Surgeon Bowes' journal (and in no other official documents) was James Baughan, the son of John Baughan and Mary Cleaver. He was born during the voyage, baptised after landing at Port Jackson on 27 March 1788 and died the next day.
* information from Mollie Gillen, The Founders of Australia: A Biographical Dictionary of the First Fleet (1989), pp 27-28
'Baughan, James (c. 1787–1788)', People Australia, National Centre of Biography, Australian National University, https://peopleaustralia.anu.edu.au/biography/baughan-james-30200/text37480, accessed 1 December 2023.
27 March,
1788
(aged ~ 1)
Sydney,
New South Wales,
Australia
Includes subject's nationality; their parents' nationality; the countries in which they spent a significant part of their childhood, and their self-identity.
Includes the religion in which subjects were raised, have chosen themselves, attendance at religious schools and/or religious funeral rites; Atheism and Agnosticism have been included.