The records for Falkirk West stop in 1855 so if they had more children after Mary Elizabeth, they aren't listed
This is probably related to the fact that statutory civil registration of births, marriages and deaths started in 1855. Before then, the only records kept were the churches' records of baptisms, banns and burials.
There is an (incomplete) index to pre-1855 baptisms and births from 1855 to 1874 at
www.familysearch.org but it does not list any children of William Hardie and Ann McAlpine.
Do I take it that you have failed to find a record of Mary Elizabeth arriving in NZ?
I will be astonished if a girl born in 1853 married in 1866, at the age of only 12 or 13. It was legal in Scotland for a girl to marry at 12, but I have never come across a reliably documented case in the 19th century. How old does her marriage certificate say she was in 1866?
Her name also gives pause for thought. It was unusual in the early 19th century to give a child two names, and when this was done, the second name was usually a surname from an earlier generation of the family. I see that the NZ DIA marriage index lists her as Eliza. Why do you think she was
Mary Elizabeth?
What does her marriage certificate say her father's name and occupation were?
The NZ DIA deaths index lists the death of an Elizabeth Keane in 1907, aged 67. This, if correct, suggests a date of birth in 1893 or 1840, which makes far more sense. Is this the death certificate you have?
There is a family in the 1851 census (transcription at
https://www.freecen.org.uk/cgi/search.pl) consisting of John Hardie, 34, nailer; Elisabeth Hardie, wife, 34; children John, 13, apprentice nailer; Elisabeth, 11; Ann, 9; Jane, 6; and Mary, 4. In the index to the 1861 census John, 43; Elizabeth, 44; John, 23 andd Mary, 13 are still in Falkirk, but Elisabeth Jr, Ann and Jane are not in the household, so must have left home - could one or more of them have gone to NZ?