Birdwood is not a family name for us. I wondered where it came from too. I think he was named after Lieutenant General Sir William Birdwood- ‘Soul of Anzac’ on Gallipoli. His father Edward Fishwick was at Gallipoli and I think it was either out of respect for what the General did for all the Diggers or perhaps there was something on a more personal note. Sadly I don't know.
From what I read General Birdwood was a great man to be related to.