I take it Catharine immigrated with her parents and that's why I can't find deaths for them in Edinburgh are between 1855 - 1940
I did find on Ancestry a Catherine Scott born to George Scott and Martha Lawson in Edinburgh December 1851!
I also found that family on 1851 census.
As you can see George is a coachman. What did catharine call her kids? sometimes you can workout her parents names by the way the kids have been named!!
Piece: SCT1851/685 Place: St Cuthbert's -Midlothian Enumeration District: 10
Civil Parish: St Cuthberts Ecclesiastical Parish, Village or Island: Barony Of Canongate
Folio: 702 Page: 12 Schedule: 53
Address: 125 Pleasance
Surname First name(s) Rel Status Sex Age Occupation Where Born Remarks
SCOTT George Head M M 38 Coachman Midlothian - Edinburgh
SCOTT Martha Wife M F 36 Midlothian - Edinburgh
SCOTT George Son U M 17 Glass Cutter Midlothian - Edinburgh
SCOTT John Son - M 15 Hosier Midlothian - Edinburgh
SCOTT Margaret Dau - F 12 Scholar Midlothian - Edinburgh
Page: 702/13 SCOTT James Son - M 10 Scholar Midlothian - Edinburgh
SCOTT Mariann Dau - F 3 Midlothian - Edinburgh
SCOTT William Son - M 1 Midlothian - Edinburgh
It might be worth your while paying to have a look at the 3 Catherine Scotts that are living in Edinburgh in 1861 on scotlandspeople.
1 1861 SCOTT CATHERINE F 7 ST GILES EDINBURGH CITY/MIDLOTHIAN 685/04 046/00 007
2 1861 SCOTT CATHERINE F 10 NEWINGTON EDINBURGH CITY/MIDLOTHIAN 685/05 029/00 013
3 1861 SCOTT CATHERINE F 8 STOW /MIDLOTHIAN 699/00 007/00 003
Not sure if any of this helps