The passenger lists to South Australia from that era did not name the passengers who travelled in steerage, i.e. assisted passengers. These passenger lists that can be seen online, such as the Bound for South Australia site, are reconstructed from other records, including:
State Library of South Australia, Adelaide. Register of emigrant labourers applying for a free passage to South Australia, 1836-1841. A copy of Colonial Office Records held in the Public Record Office, London, England.
These applications for assisted passage have the name of the head of the household, usually a man, that person's occupation and location at the time of application, and they include the numbers of male and female passengers travelling on that application, and their ages. There will be a date on that application and it needs to be checked in this case, to confirm that the date of application is earlier than the date of Jeremiah's burial in Kent. There may also be some indication on the page that only one person travelled on that application, although I think that is unlikely.
It should be pointed out that this was a very large body of work, and in some cases where limited other records are available, errors have been made. These passenger lists were also reconstructed at a time when there was very limited information available online and in electronic databases. The person who performed a great deal of this work is now deceased, so there is no way of knowing her sources. However in the case of Jeremiah Morphett, the Genealogy SA online database includes an application and embarkation number, so that record for the reconstructed passenger list did come from the assisted passage applications above.