There was one marriage of a JOHN McKenzie to a JEAN Scrymgour in Dundee 12 Nov 1821 (could be anyone though) also there is a John McKenzie on the High Court Criminal Indexes tried in 1822 Dundee for Bigamy (alias McPherson).
M(a)ckenzie is one of the commonest surnames in Scotland. John is the commonest male given name, and Jane/Jean is one of the commonest female gievn names.
There were 14 John M(a)ckenzies in Dundee in 1841, and 42 more in the rest of Angus. There was a J*an* on the same census pages as 25 of these John M(a)ckenzies, so you are not going to get very far trying to identify your Esther that way when you cannot even be sure that her parents were in fact John and Jean/Jane.
If this information at her death is accurate, Esther was born 1831 and arrived in Australia in 1845.
https://trove.nla.gov.au/newspaper/article/226979308
The one in the household with Daniel McKenzie in 1841 looks promising but that doesn't tally with the information saying that her mother was still alive in Dundee in 1850. Daniel McKinzie married Christian Yeaman in Dundee in 1801.
Christian Yeaman or McKenzie, aged 59, wife of Daniel McKenzie, harbour porter, was buried in the Howff, Dundee, on 26 January 1841.
Strange - I can't find an 1851 or 1861 entry for a Robert & Esther Adams nor is there an Adams birth on SP 1849-1854 with mmn McKenzie.
She's indexed in 1851 as E
aster Adams, aged 31, living with mother-in-law Isabella Cargill, husband Robert Adams, baby David Adams and two lodgers in Dundee in 1851. Haven't found her in 1861.
Esther Adam or Mackenzie or Pirie died in Dundee St Mary in 1898 aged 79, mmn Yeaman. Easter Pirie is in Dundee in 1891, aged 68, but I have not found her in any other census.
So I think you can safely eliminate the Esther McKenzie in the 1841 census in Dundee. You could look at that 1898 death certificate which will probably confirm that her father was Daniel.