It looks like Mary Watson and William Nicoll were not married. It was quite common in Scotland for an illegitimate child to grow up with their fathers surname and their daughter Ann appears to be the only child.
When Ann married she names both as her parents and William's occupation is given as 'Gold Digger'. Since the 'Gold Rush' in the US started in 1848 and in Australia in late 1850 I suspect William Nicoll was one of the thousands who went to try his luck in one of the 2 countries presumably never to return to Scotland.
Mary Watson (bc.1825 Fordoun) is shown as unmarried on both 1851 and 1871 census (living with married daughter 1871) and I think she died 20/8/1878 in the Poorhouse, Stonehaven of 'Disease of the Heart' - again, shown as a single woman. This shows her parents as David Watson and Catherine Skene.
Her parents married 15/12/1821 Fordoun, Kincardineshire - a son James born 1822 (familysearch) and Mary b.15/4/1824, bp.25/4/1824 Fordoun (familysearch).
I think William Nicoll will remain an enigma - since he appears to have already gone digging for gold by 1851 nothing is known about him - not his age or where he came from.
Why do you think that William Nicoll may have originated in Aberdeenshire? Certainly both Mary Watson and their daughter Ann were born in and lived in Kincardineshire all their lives.
Annette