I had a better look at the Myheritage website for the Australian Barnetts that I gave you, and decided there were too many problems, so I have worked through the NSW BMD index.
My real interest was in the naming (middle names) of the children, which can be useful from a genealogical perspective. Obviously some names come from the Barnett family (Irish), but you will see a son named Robert Duncan Kerr BARNETT, which has me wondering if this might provide a lead in finding Agnes Kerr's father.