Possible census entry for Catherine from 1861, corresponding with her birth year and also birth location indicated by husband John:
Colin Archd Mackenzie 33, minister Scots Church b. Scotland
Catherine C Mackenzie 5 b. Tynemouth, Northumberland
Sarah F Sudder 21, servant
Address: 5 North Place, Tynemouth, Northumberland
RG9, Piece 3840, Folio 29, Page 54
Trying to find Catherine/Kate in later censuses brings up this likely entry for 1871. Father Colin is showing as John on this transcript - not sure why. The younger children's birth registrations on IGI show parents as Colin Archibald MacKenzie and Mary Gilfillan and these children match what is on this 1871 census entry:
John A Mackenzie 43, Minister Govan Free Church, b. Edinburgh
Mary Mackenzie 38 b. Edinburgh
Kate C Mackenzie 15, b. England
Jessie F Mackenzie 13, b. England
Colin A Mackenzie 4 b. England
Agnes A Mackenzie 6 b. Govan
Alfred Mackenzie 4 b. Govan
William L Mackenzie 3 b. Govan
Christina T K Mackenzie 8 months b. Govan
Wilhamina Campbell 22, servant
Jane Beatie 19, servant
Address: Free Church Manse, Govan
Parents look to have married in 1851. There is this entry showing on IGI:
Mary GILFILLAN (father Walter GILFILLAN) married Archibald Colin MACKENZIE on 17 April 1851 in Saint Cuthberts, Edinburgh. Mother Mary and sister Jessie F. look to have been away from home for the 1861 census as they didn't show on that entry, just Catherine and father.
Monica