Yes the LDS Ref is the correct Catherine.[daughter].
Sorry should have put the alternative spelling for Macpherson/McPherson/M Pherson,varies considerably.
Catherine lives with her father John age 4,1851,widower 43,both visitors at 70 Bell St New Monkland,Lanarkshire. 1861John age 52 she is 15, lodgers of Isabella White,21/25 Kirk St Calton,Glasgow.John remarries 1865,his daughter Catherine marries a Thomas Docherty,dies 1924