I am also g-g-grandaughter of Matthew Galbraith b.1806 in Tralee Ireland (a shoemaker). If you're still on this site I would love to know his fathers name and birth/death dates? (and mother if you found this).
Kath
Matthew's birth details are on this site
https://churchrecords.irishgenealogy.ieThere are two entries
For one the Register has not yet been imaged
Father John Galbraith
Mother Elizabeth?

I think you will be able to get a copy of the register by following up and purchasing using reference in the entry
Book Number Page Entry Number Record_Identifier
1 41 N/R KY-CI-BA-15297
The second entry has the register imaged.
From same site an Elizabeth Galbraith dies aged 85 in 1869. Not imaged yet but could be worth a look. She would be of an age to be Matthew's mother