Amy - this could just be your lucky day. ;D
I reckon I have found the answers (or a few of them anyway) for you.
Method:-
I originally found Johannah's marriage details in the St Ives Online Parish Registers where she indicated a birthdate of about 1818 and nominated her father as Anthony Woolcock, fisherman.
I tried to find the family in the 1841 Census but have not been able to find them.
However, undeterred I decided to search through the St Ives marriages again to see if I could find any more children of Anthony.
Margery Noall Woolcock married John Mann at St Ives 8th November 1846
Peter Woolcock married Fanny Veal at St Ives 19th June 1853
Mary Ann Woolcock married Robert Smith at St Ives 6th June 1854
Anthony Woolcock married Mary Crichley Stevens at St Ives 15th August 1861
All were children of Anthony Woolcock, fisherman.
1851 Census
Teetotal Row, St Ives
Anthony Woolcock, head, mar, 58, fisherman, ST IVES
Margery do., wife, mar, 57, St Ives
Peter do., son, unm, 27, fisherman, St Ives
1861 Census
Bunks(?), St Ives
Anthony WOOLCOCK, head, mar, 68, fisherman, MARAZION
Margaret do., wife, mar, 66, St Ives
Anthony do., son, unm, 25, fisherman, St Ives
I cannot find Anthony or Margery/Margaret in the 1871 Census.
Found sons Peter and Anthony but have not noted those details just yet as I will likely find a few of them in the Baptism Register.
The 1851 Census was able to tell me a couple of things.
1. that I had found the right family because they wer in Teetotal Row and daughter Mary Ann was of Teetotal Row when she married. And also Anthony Woolcock men were not exactly falling off trees.
2. I believe I now know the name of Anthony's wife MARGERY NOALL.
The only one remotely close in IGI is:-
Margery NOALE bp. 25th August 1795 St Ives d/o Philip
From here I can, so far, get nowhere as there is no marriage for Philip any closer then 1766 and there are no other children for Philip remotely close.
However, we can pursue that problem later.
The next bit of news is about Anthony.
In the 1851 Census Anthony's birthplace was recorded as St Ives.
In the 1861 Census his birthplace is now MARAZION.
IGI shows only six entries for Anthony Woolcock but the good news is that I reckon they show the one we are after.
Remember that Marazion is/was basically part of St Hilary Parish.
Anthony Couch WOOLCOCK bp. 15th July 1792 at St Hilary son of Peter and Ann
;D ;D
From Phillimore & Taylor
Peter WOOLCOCK, mariner, m. Anne COUCH 20th January 1785 at St Hilary
The list of children for Peter and Anne now looks like this:-
Ann bp. 4th December 1785 at St Ives
Peter bp. 20th April 1788 at St Ives
Anthony bp. 15th July 1792 at St Hilary
Joanna bp. 14th February 1796 at St Hilary
There may be others but I have not yet found them.
I hope you have plenty of time on your hands because I think you are going to need it. ;D
Will finish this note off now and have a break for a little while and then I will pursue it a bit more and post my further findings.
REMEMBER - everything here, and in the following, will need verification from sources more reliable than IGI but I think you will find the bulk of it will be 'just fine'.