Research does cost money. This girl does not appear with her parents in the census so yes I feel you will eventually need a cert to confirm parentage. You often mention in your lookups that you are looking for original records. If you are looking for originals you do need to purchase them. We can only help you with transcriptions and index information. If you require copies of original records you do need to purchase them.
Yes I did find a record of John and families immigration, but I do not believe this online transcript. It needs to be viewed at the library as another source does list Josepha not Joseph. I am curious as to the age, which does not fit with anything we have.
Since they emigrated in 1850 this is the only census they appear on
http://www.slsa.sa.gov.au/fh/passengerlists/1850Agincourt.htmhttp://www.familyhistorysa.info/shipping/passengerlists.htmlObviously these ages are not correct as William was 5 in 1841 and Angelina was 3, still if this 6 is what appears it does not fit with a child born in 1837. Ages were often taken from the time the family applied to emigrate so I would expect ages may be little out. (The older two children within reason but Josepha listed as 6)
Looking at Josepha's marriage record she was 21 in 1861 (father JOHN) and 42 at death in 1882
I am flat out with grandkids this week. Suggest you do a thorough look for any later birth possibly mistranscribed in FreeBMD
There is Jerusha LADNER 1842 but its not her - she appears in 1851
Kris