We're in the same situation at the moment and I recently looked into it as DD and I just took a trip to visit the rellies on the UK. Your DD is born an Australian citizen and is entitled to both Aussie and UK passports - she would use the Aussie passport leaving and entering Australia and her UK passport in the UK, so there is no need for her UK passport to have details of her Australian status, iykwim? It's the same as if you become citizens and are no longer required to carry an Australian visa in your UK passport.
Incidentally, she also doesn't need a UK passport to travel to the UK - it's a much longer processing time than the Australian one so when we went DD just travelled on her Aus passport as I didn't want to run the risk of complications arising if the UK passport arrived while we were over there, so I decided to just wait until we got back to apply for it.
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