I'm pretty sure that as she was born here to permanent residents then she has a right to citizenship automatically. So if you are applying for a UK passport then she would be a dual citizen. My son is a little different as he has an aussie dad (I'm British), but I have both UK and Oz passports for him and he is a dual citizen.

This is from the citizenship website:

Australian citizen by birth

Whether you are an Australian citizen by birth depends on the date of your birth.

Most children born in Australia before 20 August 1986 are Australian citizens by birth unless one parent was entitled to diplomatic privileges or was a consular officer of another country.

Children born after that date are only Australian citizens if at least one parent was an Australian citizen or permanent resident at the time of their birth.

Children born in Australia to parents who are not Australian citizens or permanent residents, automatically acquire Australian citizenship on their 10th birthday if they have lived most of their life in Australia.

We have very lucky kids to be citizens in Australia and the EU!!