Hello Marie,
I think your John Gilmour, has moved from Kilmarnock, to Stewarton, by 1851,
on the 1851, census index, for Stewarton, is the following family,
Gilmour John, aged 66 years,
Gilmour Margaret, aged 47 years,
Gilmour Adam, aged 15 years,
By 1861 the family are still in Stewarton,
Gilmour John, aged 77 years, born Fenwick,
Gilmour Margaret, aged 57 years, born Fenwick,
Gilmour James, aged 21 years, born Kilmarnock,
Gilmour Robert, aged 16 years, born Stewarton.
In another part of Stewarton,
Gilmour Adam, aged 25 years, born Kilmarnock,
Gilmour Mary, aged 18 years, born Stewarton.
Dont know if this is Adam, and his wife.
In 1841, this family were living at Laig Blackwood, in Kilmarnock, they had three kids with them, Adam, aged 5 years, Agnes, aged 3 years, and James, aged 1 year.
In the whole of Ayrshire, there was only one Adam Gilmour, in 1851.
Regards,
Jonn.