According to census Elizabeth was indeed born 17th December but in 1866 Glasgow, one of at least 8 children:
Jane bc.1855 Glasgow
Patrick b.16/10/1857 Hutchesontown, Glasgow, d.1858
Andrew b.6/5/1860 Tradeston, Glasgow
Mary b.1/3/1862 Hutchesontown, Glasgow
John b.25/9/1863 Tradeston, Glasgow, d.1866
Elizabeth Hannah b.17/12/1866 Tradeston, Glasgow
Margaret Hanlon b.6/4/1869 Tradeston, Glasgow, d.1869
Marion b.29/11/1871 Tradeston, Glasgow.
Looks like the parents did a spot of 'practising' first as John Carlin didn't actually marry Elizabeth Golder until 24/8/1863 Hutchesontown, Glasgow!
If you pay to view the certificate it will tell you their respective parents names.
Census shows John Carlin bc.1834 Ireland and Elizabeth Golder bc.1833 Glasgow.
Annette