Hi
Both censuses 1841 and 1851 or just the 1841 census? If you accept the 1851 census then the 1841 census goes with it. Caroline the child aged 10 on the 1851 census gives her birthplace as Battersea which is where the 1841 census was and where the family still were in 1851. Caroline's mother was called Margaret who was aged 20 on the 1841 census (ages rounded down to the nearest 5 on that census) which fits to an age of 34 in 1851. The census enumerator has obviously made a mess of the name Alex (ander) but again his age fits to Alexander's in 1851 -25 in 1841 and in 1851- 36. The next child born on the 1851 census was Jane aged 8 so she wouldn't be in the 1841 census.
As far as the 1841 census goes there was a general belief that the census was a way of gathering data for the poor law and that people might in consequence end up being sent back to their place of birth. This could be the reason, as well as a hazy knowledge of county geography, that many people gave yes to the county of birth question, claiming they were born in the county, when later censuses showed they were not.
St Mary, Battersea 18th October 1836 born 10th October
Elizabeth Jane Tenant parents Alexander and Margaret Jane, Battersea, father's occupation labourer
buried at the same church 11th December 1837 aged 14 months Elizabeth Tenant
same church
9th September 1840 born same day
Caroline Tennant parents Alexander and Margaret, Battersea, father's occupation labourer
14th January 1844 born 25th November 1843
Jane Tennant parents Alexander and Margaret, Battersea, father's occupation labourer
19th April 1846 born 26th March
Harriet Tennant parents Alexander and Margaret Jane, Battersea, father's occupation labourer
1st April 1849 born 5th June 1848
Alexander Tennant parents Alexander and Margaret Jane, Battersea, father's occupation labourer
buried 12th July aged 3 1851
13th October 1850 born 23rd September
Thomas Tennant parents Alexander and Margaret, Battersea, father's occupation bricklayer
27th November 1853 born 27th September
Henry Tennent parents Alexander and Margaret, Battersea, father's occupation bricklayer
Does Alexander's Australian death certificate not specify who his parents were and therefore Ann's maiden name?
Regards
Valda