Could it have been Ballacondyn?
As her marriage was in Australia it could be a misspelling. - But even in the IoM the same name was often spelt differently.
Have a look at Bride place names on Manx Notebook:
www.isle-of-man.com/manxnotebook/fulltext/pn1925/be.htm

Thanks to the M.I. we know that Catherine was still alive in 1851 which is the first census which includes places of birth and relationships.
Indexes are at:
www.iomfhs.im/lawsons/census/census_index.html
If you don't have access to census scans you can see who is in the same household by the refs in this index.

The 1851 census for Bride has Ballacrink House at the top of the column where the Callow family is the 3rd household:
Daniel Callow, Head, U[nm], 53, Shoemaker, b. Bride
Catherin Callow, Mother, U, 77, Tradesmans widow b.Jurby
Mary Callow, Aunt, U, 80, Tradesmans daur., b.Bride
Jane Callow, Sister, U, 50, Tradesmans daur., b.Bride.

Having the aunt there b.Bride is a bit of luck because it should make it easier to find which John Callow he was, even though he died pre-censuses.

In the 1841 Bride census [adult ages rounded] Catherine Callow aged 75, Ind., is living with 3 servants (no place name). The place name of the next entry may be the one you are looking for - it looks like Ballayonage, but someone who knows Bride places better than I do might correct me.

The last two places on the previous page are Ballaquark and Ballacottier. The Cottier family (John, 50, a yeoman, Catherine, 35, and their children) are at Ballacottier, and are the household immediately before your Cath Callow's entry, with a single line between them, which indicates that they were on the same property. (Double diagonal line at the end.)

Have just checked the IGI on FamilySearch, and the youngest child Elizabeth was bapt 8 Nov.1840 Bride, daur of John Cottier and Catherine Callow! Could this Cath be John and Cath's daughter?
John Callow and Catherine Cormode married on 17 Aug. 1793 Bride. Even though little information is given in the register at that time it could be worth looking at the entry to see whether there is a place name or Callow witness. It is on LDS film no.0106713 which can be ordered to view at their Family History Centres worldwide. (See phone book for Church of Jesus Christ of Latter-Day Saints.)

Re. Mary Callow the aunt, above, there are two possibilities bapt Bride. One the daur of Danl Callow & Mary Camaish bapt Jan 1771, and the other bapt 10 Jan. 1773, daur of William Callow & Jane Christian, but no obvious brother John of the right date.

Sue