Hi, moved out here a couple of months ago, and wanted to give a bit of info for anyone with younger kids making the move. In Oz, all children under the age of 7 have their immunisations recorded on the Australian Immunisation Register; every time they recieve a vaccination, the doctor fills out a form, sends it off, and your childs records are updated. To claim certain benefits, such as help towards childcare costs, your children under 7 need to be on the register, and up to date with the Australian vaccination programme. When you arrive, if you make an appointment to see a doctor, and take your red book from England, the doctor will fill in an Immunisation History form, send it off to the AIR, and you will recieve reminders when your child is due any immunisations.
The Australian immunisation programme varies a little from that in England; in Aus, they immunise against Hep B, which is not offered in the UK, so all my kids are now on a catch up programme. Our UK GP was not so clever in filling out my kids records in their book, so it would be a good idea to check that everything they have had is recorded. If you want to get your kids in kindy, you can get about 70% (varies) of your fees paid, depending on if you work, how many kids you have etc, if their immunisations are up to date.
Alternately, if you did not want your kids immunised for any personal beliefs etc, you can get a form that states you object conciensciously.
Sorry for the essay, but I found this out the hard way (doctors filling forms out wrong etc) and if it helps one person I'm happy.