I have a possible family for 1851 Census which would indicate that Jane/Jean Stoddart is dead.
86 Clyde Street, Anderston, Barony Lanarkshire
Neill Munro head age 21 M Grocer Born England
Amelia Munro wife age 20 U Grocer's wife Born England
Elizabeth Munro Dau age 1 U " "
John Burnside Visitor age 35 W Agricultural Labourer Born Renfrewshire, Kilpatrick
John Burnside Visitor age 11 U Scholar Lab's son Born Glasgow , Lanarkshire
Elizabeth Burnside Visitor age 6 U Scholar Lab' Dau Born Renfrewshire, Greenock
Ann Mathieson Visitor age 35 M General Servant Born Courthill, Ross & Cromarty
These look like good candidates for the family.
If Jane/Jean Stoddart has died between Elizabeth's birth and 1851 Census, it is unlikely that you will find a register of her death.

Looby
