I can't find your GG Grandmother, Frances Maitland in my family tree. But there is a branch of the Dundrennan Maitlands which was started by a brother of my GG Grandfather b1801 who emigrated to Otago, which I think is near Dunedin. Although all his descendants are accounted for, and none is called Frances, it is possibly that your ancestors were in some way connected.
Are you in New Zealand yourself?
You could try contacting the Clan Maitland secretary in NZ, Judette Maitland, at email@example.com