As this is in response to a posting dated 2004, I hope that you are still interested.
My mother, Elvie Irene Tournier, often spoke of a Bonnie, Laurie (my spelling) and Tommy Tournier so often that I thought they were her brothers and a sister. So, when I began tracing the family tree, I was surprised to find that they did not appear to be in it. Not only that, but I could not find any records of their births, marriages or deaths. I then began to think that they must be cousins and/or possibly, born overseas.
However, I did find a number of references to Lawrie (the jockey)in the newspaper archives. Indeed, the last entry referred to him winning a few races in NZ. My mother told me he was a jockey and that Tommy (?)was a trainer. In her later years, my mother and her younger sister Eileen used to visit a Bonnie in Geelong and, when Eileen died, I found an address for an Albert (no surname): Te Kowhai, Road 8, Frankton, New Zealand.
Without going into detail, I can confirm that our family originally came from Switzerland, first migrated to England and later migrated to Australia from there. Bill, the relative in Queensland is most likely my mother's brother William (who did like the races).
We may be able to help each other to fill in some gaps.