I think you'll find the child will have to apply for citenship first if born outside Australia to an Australian parent.If one parent is Australian, and the child is born in the UK, the child will normally be Australian. Just need to register it. I can't recall how we did that, so long ago now.
Father British, Mother Australian, child born in UK. Child had two passports very quickly, UK and Australian.
No need to add on to visa application, just arrange a passport.
But if the visa has not been finalised by the birth, upload the birth certificate as extra proof, at the time.
Talking about hospitals, Lewisham Hospital was great for children.