I have sent Deb a PM with the information I found at the Archives yesterday. I looked and looked but could not find Elizabeth Anne or Rose - tried various spellings, everything.
As Deb's estimate for her birth was so close to their arrival I thought she may have been born on board the ship but there was no mention on the film of any births. In fact there were only 39 women on the ship.
There is usually a summary at the end of the "log" (or whatever it's correct name is) with this information, and there was only one female death recorded. All free, no assisted migrants, only a couple of hundred people on board so she couldn't have got lost!
I guess Elizabeth may have been born within days of arrival in Australia, and with all the fuss of arriving in a new country, perhaps she was never registered? Maybe the family didn't know they needed to register her birth or how to go about doing this. Just a thought.
Maybe someone else has some ideas?