I am descended from Joseph Moorhouse (b abt 1792) and Easter Kaye (b abt 1799) who lived in Fulstone. They did not have a daughter Jane so I don't see an immediate link. Also, Joseph was an illegitimate son and his mother married some time afterwards. However, this does not rule out a connection further back and I have a fair amount of detail on Joseph's ancestry.
Do you know when Jane married Nathan Gill, and do you have the marriage certificate? This should at least confirm her father.
If you can give me any more detail I will be able to look and see what else I can find out.