Hi John, I think I've found Janet's parents in 1861 index.
According to LDS site the are some of the children of William and Margaret.
15. Walter Watson - International Genealogical Index
Gender: Male Birth: 1835 Shotts, Lanark, Scotland
16. William Watson - International Genealogical Index
Gender: Male Birth: 1837 Shotts, Lanark, Scotland
17. James Watson - International Genealogical Index
Gender: Male Birth: 1843 Shotts, Lanark, Scotland
18. JANET WATSON - International Genealogical Index
Gender: Female Christening: 05 DEC 1833 Shotts, Lanark, Scotland
19. MARGARET WATSON - International Genealogical Index
Gender: Female Christening: 30 OCT 1831 Shotts, Lanark, Scotland
1861 names index. Census taken SHOTTS
William Watson age 55 born Crawford LKS
Margaret age 63 born Muirkirk, Ayrshire
Walter age 25 born Shotts
William age 23 born Shotts
James age 18 born Shotts
James Braidwood age 3 born Shotts
John Ross age 55 born Carnwath, LKS (I think this is Margaret's brother) see below
Also on the IGI site there's a christening for a Margaret Ross in Muirkirk.
Margaret Ross......ch. 13th aug 1798 Muirkirk
parents........Philip Ross and Jean Brown.
If you check for children of Philip and Jean you will also get a 'male' Ross born Carnwath 1805 whiich fits the John Ross in the census.
As for Janet Watson I think this is her, but she's not with family
Census taken Shotts
Janet Watson age 24 born Shotts
Have fun checking it out
Liz