I went through all the original images for Burgh by Sands in 1851, in case she had gone back to where her parents were. Then I thought that if her daughter was in Orton, maybe she was there too, so I trawled through all of those pages as well.
I think that checking every original image for Carlisle might be too daunting!
I've looked for Tamar, Thamar, Tamer, Tammer and various other possible spellings and I've checked Scottish records in case she nipped across the border.
But absolutely no joy whatsoever. Maybe she did emigrate and maybe the Jane in 1851 isn't her daughter?
Sorry, I'm not being much help here.
