This source as I'm led to believe is from My Heritage. Where is the actual baptism record?? To support the fact that Joseph Cope is her father. It's most likely that Jane Cope's mother-is Fanny Cockersole, however the father is unknown. She was possibly pregnant when marrying Joseph Cope. To verify a baptism record you require to see the actual record, from where this information has derived from.
Another global genealogy website - Wikitree.com with over 34m members has stated that the site for Jane Cope is false. She has been removed as the child of Joseph Cope, until there is an actual birth/baptism record with citations (image of) has been found.
The actual baptism record needs to be cited.
I do hope that this helps, and until such time that the actual record is cited, Jane Cope should be omitted as the child of Joseph Cope. Please see his profile on WikiTree.com. His ID on WT: Cope-3038