Hi
A search on the 1841 census (you can access it via Freecen) shows a George Carlyle, aged 9, in Dornoch village, Dumfriesshire. Unfortunately, the 1841 doesn't show relationships but the head of household appears to be a John Carlyle, aged 45, a farmer and bacon dealer, land proprietor and miller. There is no female listed who might be a mother/wife.
On the 1851, the family are still in Dornock, and George is listed as 'son' of John, no mother.
A search on Scotlands People
www.scotlandspeople.gov.uk shows this baptism:
21 Jan 1832, Dornock, Dumfriesshire George Scott Carlyle, s/o John Carlyle and Marrianne Sloan
This is the only George Carlyle with that approximate birthdate in Scotland in the two censuses and the only one appearing in the baptisms, 1830-1835 (all parishes, all counties) using Carl*le .
Regards
Gadget