I am not really related to Richard W Davis and Mary Craigie. I was only looking for Jane's birth because of Andrew's remarriage to her after Sarah Foulis (the sister and daughter of my ancestors).
When I saw that Jane's mother was a Craigie I thought I'd investigate further, however I didn't quite make the connection as you had.
Sorry I don't know which ship she arrived on, but many of those people from Orkney were seafarers so she may have been a crew member, I'm not sure if females were crew members in those days... But if she was it'd explain why there's no record of her arrival.