A couple Jane Kennedys that might be worth looking at, based on Ancestry's indices. Neither is a perfect match but each has bits that are intriguing......
Jane Kennedy
Age: 19
Estimated birth year: abt 1832
Where born: Ardrossan, Ayr
Occupation: Employed At Home
Parish Number: 590 Civil parish: Dundonald County: Ayrshire
Address: Ploughland ED: 1 Page: 25 Household schedule number: 84 Line: 12 Roll: CSSCT1851_131
John Kennedy 33 head b. Kilmaurs farmer of 120 acres
Jane Kennedy 37 wife b. Stevenston
Margaret Kennedy 24 daughter b. Ardrossan
James Kennedy 26 son b. Ardrossan employed on farm
Mary A Kennedy 21 daughter b. Ardrossan
Jane Kennedy 19 daughter b. Ardrossan
Agnes Kennedy 17 daughter b. Ardrossan
Hugh Kennedy 15 son b. Ardrossan
Alexander Kennedy 13 son b. Dundolald
Robert Kennedy 11 son b. Ardrossan
John Kennedy 13 son b. Ardrossan
Jessie Kennedy 9 daughter b. Ardrossan scholar
Laurence McCallum 24 servant b. London, Ayr
(I didn't look at the original at SP, to see what is up with the ages of the parents vs. those of the oldest children.....I'm guessing a mistranscription somewhere.......)
Jane Kenedy 22 b. Ireland
Res: Stewart Place Sorn, Catrine, Ayrshire
ED: 3A
Page: 14 (click to see others on page)
Household schedule number: 52
Line: 2
Roll: CSSCT1851_138
occ. hand sewer
Rest of household:
Cleanor Kenedy 47 b. Ireland head occ hand sewer
Catherine Kenedy 20 dau b. Ireland hand sewer
Eleanor 12 b. Ireland hand sewer
Anne 9 b. Ireland scholar
John 6 son b. Ireland at home
Arthur Jones 50 b. Ireland brother Chelsea pensioner
BJ