Re-scanned image nothing like Gillespie for mother Catherine! So, not the family from Gigha.
I agree, McArthur is likely name (with McCarter and all the variants). There is only one other Neil and Catherine McGougan family, apart from the Gigha family.
These are these children showing on IGI to a John McGougan and Catherine McArthur:
1. MARY MCGOUGAN Birth: 06 SEP 1860 Cumlodden, Argyll
2. DUNCAN MCGOUGAN Birth: 08 OCT 1861 Cumlodden, Argyll
3. SARAH MCGOUGAN Birth: 14 OCT 1863 Cumlodden, Argyll
4. ISABELLA MCGOUGAN Birth: 21 JAN 1866 Cumlodden, Argyll
5. JOHN MCGOUGAN Birth: 03 FEB 1872 Cumlodden, Argyll
From the 1861 Census:
Neil Mcgougan 43, Miner Of Nicol, b. Inverary, Argyleshire
Catherine Mcgougan 26 b. Kilmichael Par, Argyleshire
Catherine Mcgougan 3 b. Kilmichael Par, Argyleshire
Margaret Mcgougan 1 1/2 b. Uist, Inverness-Sh
Mary Mcgougan 7 Months
Duncan Mckellar 50, lodger, tailor b. Kilmichael Par, Argylesh
Mary Mckellar 49
Catherine Mckellar 13
Duncan Mckellar 12
Address: Auchindrain, Cumlodden Argyll
Can't easily see Catherine and Margaret's births on IGI. Parents only look to have married on 14 JUN 1860 Inveraray And Glenaray, Argyll (IGI).
Monica