So back to Elizabeth, this
should be yours (in fact there was a 3rd candidate, born and christened in Sep 1841 but I've ruled her out as she's still at home with parents John and Hannah in 1861):
1851HO107/2066 143 22
Bedworth, Warwickshire
New TownJames Pickard, head, 39, Ribbon Weaver Silk
Judah(?), wife, 40, ditto
Joseph, son, 13, ditto
Elizabeth, dau, 11, ditto James, son, 5
Allis, dau, 3
John, son, 1
All born Bedworth.
I'm wondering if it's someone's 2nd marriage, with the 6-year gap between the kids... (Edit: doesn't look like it

)
Extracted IGI christening
ELIZABETH PICKARD
Birth 07 DEC 1839
Christening 18 OCT 1842 Bedworth, Warwickshire
Father JAMES PICKARD Mother JUDITH
IGI extracted marriage:
JAMES PICKARD - JUDITH CATTLE
Marriage About 20 AUG 1832 Bedworth, Warwickwhire