I don't know about your Jane's baptism, but there was another FITZWALTER around the same time zone in Newcastle, who could possibly be related:-
FITZWALTER, Francis Forster Christening
Sex: Male
Christening Date: 22 Feb 1789 Recorded in: Saint Nicholas Parish Reg. And Nonconf., Newcastle Upon Tyne, Northumberland, England
Father: Thomas FITZWALTER
Mother: Isabella
Source: FHL Number 1068902 Dates: 1678-1844
There was also one later in Sussex:-
FITZWALTER, Elijah Christening
Sex: Male
Christening Date: 9 Nov 1825 Recorded in: Steyning, Sussex, England
Father: John FITZWALTER
Mother: Mary
Source: FHL Number 1068527 Dates: 1792-1925
Harry