I'm curious where you found the census data that you noted:
CENSUS of the couple and their children:
1861>1901
I didn't find that on the FreeCEN page, and at Family Search I've only seen individual entries, not households.
FreeCEN is an ongoing project & doesn't have all years for all shires/burghs; 1841 is the most complete all round, followed by 1851, a smattering of other years. There are other (subscription) sites where either all Scottish Census are available as transcribed records for each 'household' together, or on Scotlands People as images (once you've found the right people through their search engine).
I had presumed you already had all these census 1861>1901. If you would like me to type up & post each household in each one, just let me know !
It's interesting that this Robert Walker is listed as being born in Islay, Kilbrandon, and Easdale. Easdale is part of Kilbrandon, but Islay is a different place.
"Islay" is what has been transcribed by a pay site. To be 100% sure this is what is written down in the enumeration book, you'd have to check the original image.
I haven't been able to find a record of his birth. I've checked the records at Scotlands People (Old Parish Registers and Catholic Registers).
You may never find a record of his birth - and as it's before 1855, such a record would be of a christening/baptism as opposed to the actual birth. - and as such, a christening might occur close to a birth or in some cases, years late - or not at all. He may well have not been Established Church of Scotland (which is what the OPR's are, by and large); Catholicism whilst not impossible, would probably be less likely than other Non-conformists : Weslyan Baptist Methodist , etc. OPR or Non-Conformist records can be patchy in both survival or existence in the first place, record keeping differed from shire-to-shire and parish-to-parish, clerk-to-clerk. Read more here:
https://familysearch.org/learn/wiki/en/Kilbrandon_and_Kilchattan,_Argyll,_Scotland_Church_RecordsI haven't found any marriage record for his parents, and unfortunately haven't found any death records either.
Ditto
The story is that his father died in a quarry accident at Easdale Island and that after that, the younger Robert Walker walked down to Renfrew with his mother to start a new life.
Try and find out if there is at least a register of mining accidents in Scottish Slate mines, or if there was a larger accident at the Easdale mine in the 1840's, perhaps one which involved a number of people rather than a single incident with a single miner.
If the 1841 census entry with a Robert Walker as a 12 year old in Balvicar Village is him……………..It just seems like some random collection of people.
At the ripe age of 12, Robert would have easily been out to work at that age and away from family; perhaps he was deemed too young for the quarries, or his parents wanted to keep him away from the quarries? In any case , if that's him in 1841 (as it looks like it could be), he's been found a 'place' with the McKay family of Isle of Seil where father McKAY's occupation is "Post" - quite an important job in the wide area, keeping communications etc, and like as not ran the local store too - certainly enough to occupy both McKAY men and the 2 male servants.
The 1841 Census isn't random. And very much unusually for FreeCEN, they've transcribed the record quite incorrectly. This is how it should be, I checked the image - the 1841 household of Archibald McKAY snr:
//
Arch'd McKAY 60, Post - Y
Mary McKAY 55, - Y
Catherine McKAY 20, - Y
Arch'd McKAY 25, Post - Y
/
William GILCHRIST 20, M.S. - Y
Robert WALKER 12, M.S. - Y
Arch'd CURRIE 8 - N
//
The image shows no 3 year old Jean MAY at all, and James CLERK is the head of the next household after the McKAYS!
The household after them have been transcribed correctly, it's just a hiccup with the McKAYS.
Apparently the younger Robert Walker was born on Easdale Island and his father worked in the quarry, yet there's a document that says he was a cottar.
Take a look at the household after the McKAYS in 1841 on FreeCEN, where you will see Mary McQUEEN was the Cottar, and the men in the household were in the Quarries. Similar with many other households, quite often an older man as a Cottar, younger men as Quarriers.
Cheers
AMBLY