As to the year of Mary's birth, we can clearly deduce 1821 as her own gravestone (shown here: https://en.wikipedia.org/wiki/File:MaryMoffatGravestone.JPG) shows engraved that she "aged 41 years". If Mary died in 1862, 41 years earlier would make it 1821. As to the birthplace, an ancestral file found on geni.com (http://www.geni.com/people/Mary-Livingstone/6000000008526577762) along with many other sources show here being born in Griquatown, Cape Colony.
Date of April 12th is given in Paul Bayly's biography/autobiography "David Livingstone, Africa's Greatest Explorer" in "Key Dates"
https://www.familysearch.org/tree/person/details/MD73-GYG
The information can be found on her gravestone: https://en.wikipedia.org/wiki/File:MaryMoffatGravestone.JPG
Mary's gravestone: https://upload.wikimedia.org/wikipedia/commons/9/9e/MaryMoffatGravestone.JPG
(1) Zij is getrouwd met David LIVINGSTON.
Zij zijn getrouwd op 2 januari 1845 te Kuruman, Free State, South Africa, zij was toen 23 jaar oud.Bronnen 1, 2
Kind(eren):
(2) Zij heeft/had een relatie met David LIVINGSTONE.
Kind(eren):
Mary MOFFAT | |||||||||||||||||||||||||||||||||||||||
(1) 1845 | |||||||||||||||||||||||||||||||||||||||
David LIVINGSTON | |||||||||||||||||||||||||||||||||||||||
(2) | |||||||||||||||||||||||||||||||||||||||
David LIVINGSTONE |