Would anyone be able to recommend how I might start searching for this information as I'm quite new to family research.
Work back systematically until you have found as much as you can about the family.
Go to
www.scotlandspeople.gov.uk and invest in some credits.
Use one credit to find and five credits to download the marriage certificate of James Nicol and Agnes Davie. This will tell you the names of their parents. Also get Agnes Davie's birth certificate which, being in 1855, will tell you where her parents were born and how old they were when she was born.
This may be enough to find the baptisms of Agnes' parents, but if not, you should get their death certificates, which will tell you the names of their parents. Go for her mother first, because she should be indexed under both her married and her maiden names.
Likewise look for the death certificates of James Nicoll's parents and get the names of his grandparents. This might answer the question. There is no point speculating and guessing.
The 1881 census, by the way, lists James Nicol, 25, born Glasgow, with wife Agnes, 26, born Falkirk, son John, 2, born Falkirk, brother Alexander, 21, born Glasgow and widowed father-in-law John Davie, 58, born Falkirk. These brothers match the family of James Nicol and Helen Mitchell, whose son James was born on 13 October 1855 and son Alexander on 17 February 1860.