To ciderdrinker, heywood, Kiltaglassan, and Dundee,
Thank you all for your interest and responses.

Elizabeth/Bridget Laurenson ms Gallacher seems to have died between 1891 and 1900, from information given on the marriage or death records of her children. The death in Bressay in 1866 is not her. Actually, the surname Laurenson is quite common in Shetland and there seem to have been a number of quite large families with that surname.
I did not want to make the initial post too long, but as some of you have already noticed there is an error in the 1861 Census with the name of the youngest child who appears as Jessie A aged 6 months born Leith. Actually 'Jessie' or Janet A was born in 1858 Lerwick Shetland and would have been age 3 in the 1861 Census. However, a younger sibling Margaret Jean was born in Sep 1860 in South Leith and so that is who actually was the 6 month old child. Quite where the real Jessie A was staying is a little mystery.
As ciderdrinker mentioned in terms of searchng in Leitrim records for Bridget/Elizabeth's baptism it is unfortunate that we do not have names for her parents.
Sometimes, it is possible to guess the names because of a 19th Century Scottish naming tradition. However, Robert and Bridget/Elizabeth do not seem to have followed that.
The children were Robert James b 1852, Laurence Nicol b1854, Bridget Elizabeth b1856, Janet Ann b1858, Margaret Jean b1860, John Peter b1862, and James William b1864.
Their father, Robert Laurenson (1825-1899) was the son of Nicol and Janet Laurenson.
I do not know if the Louisiana Marriage record in 1852 of Robert Laurenson and Bridget Gallagher might have the names of her parents. I am trying to find out how to access a copy of any marriage certificate
Ciderdrinker is correct that the last time Bridget/Elizabeth ms Gallagher appears in records is 1864 but actually when she registered the death and burial of her infant son James William who had been born in Aug 1864. He died in Nov 1864, of 'marasmus' , essentially malnutrition or starvation.
However, 'the plot thickens'...Part of the explanation for the infant's cause of death, may be that from a Newspaper Report we know that in late Sept 1864, Bridget/Elizabeth, in the context of a serious and violent domestic disturbance with husband Robert Laurenson, and while calling for help, fell out of a window 3 storeys up. She sustained injuries and concussion and was hospitalised, but I don't know for how long. She was probably no longer able to breast feed her child for some time which almost certainly contributed to his tragic death. Her husband was arrested and we are trying to find out if there was a prosecution...did she fall or was she pushed ? It was she who registered the death of her baby son in Nov 1864
By the 1871 Census her two eldest sons Robert and Laurence were most probably at sea, her daughters Bridget and Jessie were in Domestic Service in Shetland, John Peter had died in Shetland in 1868 and in 1871 Margaret Jean was staying with her paternal grandmother and aunt on Shetland....but I don't know where Bridget/Elizabeth ms Gallagher was.
There is a possibility that she was in Shetland in 1873, because there is a record of allegations of theft of clothing by Robert Laurenson made against his 'ex-wife' Bridget Gallagher. I am waiting for more details.
Anyway, sorry this has been a long post, and thanks for your interest
Morris