In the first place you are not going to find, in 1841, any details for someone born in 1843 - 2 years later!
So I assume you meant 1851 census?
Reference HO107/2475/404/5
East House, Crinow
Williams, William Head M 40 Labourer b Casheston
Williams, Margaret Wife F 39 b Kiffig, Carmarthenshire
Williams, John Son M 14 b Crinow
Williams, Eliza Daughter F 9 b Crinow
Williams, Hannah Daughter F 6 b Crinow
Williams, Thomas Son M 3 b Crinow
Williams, Edwin Son M 8 months b Crinow
Secondly, with the eldest child being born c 1837, the marriage is likely to have taken place before civil registration started in July 1837.
So you need parish registers.