Hi Kelt
For certainty and verification, as Nell suggested, their MC would confirm her parents.
There is however a family in Symington, Ayr in the 1851 Census headed by Hector,a blacksmith and Janet, mother. The household includes a Catherine age 10 which fits with the ages you have.
A parent search on IGI for a Hector Walker and Janet McCutcheon shows 11 children, those entries pre-1855 are all submitted entries. At least 4 are post 1855 and actual extract.
For Catherine Walker following her marriage to John Moffat, the following children show on IGI:
1. DAVID MOFFAT Birth: 05 JUL 1864 Beith, Ayr, Scotland
2. JANET MCCUTCHEON MOFFAT Birth: 13 AUG 1872 Blythswood, Glasgow, Lanark, Scotland
3. HECTOR WALKER MOFFAT Birth: 28 APR 1868 Calton, Glasgow, Lanark, Scotland
4. JOHN MOFFAT Birth: 13 AUG 1872 Blythswood, Glasgow, Lanark, Scotland
No.s 2/3 look direct hits for her parents' names.
............but to verify, you will still need to see her MC or DC to be 100% sure

Regards.
Monica