Find Ancestors

My husbands Great Grandmother was a Catherine Fleming who married William Snowling Stearn 30th December 1862 at St Stephens in Toodjay in Western Australia.
I have been searching for sometime for Catherine's parents, on their marriage certificate she has as her father a William Fleming a Bricklayer.
I have found on Scotlands People BMD site a Catherine born 5th September 1841 Bapt 15th September 1841 at Inverness parents William ( a Bricklayer ) & a Mary McCleod & wondered if this might be her parents?
Any help would be appreciated

1851 England, Wales & Scotland Census Transcription
60, Up Kessock Street, Inverness, Invernessshire, Scotland

Ann McLeod Head Widow Female 70 1781 Shoemaker's Widow Invernessshire, Scotland
Catherine Fleming Grand Child - Female 9 1842 School Invernessshire, Scotland

Several other children born to the same couple:

1841 England, Wales & Scotland Census Transcription
37, Grant Street, Inverness, Invernessshire, Scotland
William Fleming Male 35 1806 Invernessshire, Scotland
Mary Fleming Female 35 1806 Invernessshire, Scotland
Thomas Fleming Male 9 1832 Invernessshire, Scotland
Mary Ann Fleming Female 6 1835 Invernessshire, Scotland
Johanna Fleming Female 4 1837 Invernessshire, Scotland
Betsy Fleming Female 2 1839 Invernessshire, Scotland

1851 England, Wales & Scotland Census Transcription
46, Grant Street, Inverness, Invernessshire, Scotland
William Fleming Head Married Male 46 1805 Journeyman House Carpenter Inverness
Mary Fleming Wife Married Female 44 1807 Wife Of Journeyman Inverness, Invernessshire,
Mary Ann Fleming Daughter Unmarried Female 17 1834 House Servant At Home Inverness
Johanna Fleming Daughter - Female 15 1836 House Servant At Home Inverness, Invernessshir
Elizabeth Fleming Daughter - Female 13 1838 Scholar Inverness, Invernessshire,
William Fleming Son - Male 6 1845 Scholar Inverness, Invernessshire, Scotland
Donald Fleming Son - Male 5 1846 Scholar Inverness, Invernessshire,

First name(s) Johnna
Last name Flemming
Gender Female
Birth year 1837
Baptism year 1837
Baptism date 30 Sep 1837
Baptism place INVERNESS,INVERNESS,SCOTLAND
Father's first name(s) Willm.
Father's last name Flemming
Mother's first name(s) Mary
Mother's last name MacLeod
Place Inverness