Hi Kimberly, I am your Australian relative and have been in contact with you previously.
Like you I have been looking for a marriage of William and Esther, a birth record for Esther and also the family in the 1851 Census.
In the 1841 Census, I think you will find that William is aged 1 year, not aged 6 as is mentioned in a previous post. Perhaps in this census William possibly is 25 not 45 as in later census he drops 20 years from his listed age.
I did contact a records office about 5 years ago looking for a birth record for Esther. This is the reply that I received back:
Alexander Campbell married Hester Whitney in Alverstoke in 1816
Only children for Alexander and [H]Esther in our index are Elizabeth and James baptized in 1817, and Selina in 1822. The first two baptisms were in North Stoneham although the family was from Portsea. The third baptism was in Farlington where the father was described as a traveller dealing in earthenware. The possible inference is that being described as a traveller it meant that the family were in fact gypsies at that time, and so were highly mobile around the area which may account for the lack of baptisms.
The only baptisms I can find for Alexander Campbell is in 1813 to parents Alexander and Jane, and in 1814 to parents John and Ann, both in Portsea.
The only baptism I can find for Esther Campbell is in 1810 to parents Adam and Ann in 1810 in Portsea.
There is no marriage for William Lambour/Lambert to Esther/Hester in our marriage index to 1837 [although they may have married after this] and no baptisms for any of their children afterwards. We have baptisms indexed up to 1874. The conclusions is that the children were never baptized or maybe the family was non-conformists whose details we do not have in our index.
A number of William Lambert and Esther Campbell/Lambert's children were baptised in Surrey (Croydon). I believe that there is also a daughter Sophia Lambert, baptized 25 May 1845. She died as a child and was a quite unexpected find when researching the family.