There is no BDMH record of this. On the births fiche there are 3 possible births in that area but 3 are accounted for as being to different parents.

Therefore need to search in Denmark.

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Carrington Hospital, now Unitec Institute of Technology.
Whau Lunatic Asylum ‏(or: Lunatic Asylum at the Whau; later: Auckland Lunatic Asylum, Avondale Lunatic Asylum, Avondale Hospital, Auckland Mental Health Hospital, Oakley Hospital; Carrington Psychiatric Hospital; commonly Carrington/Oakley Hospital)‏‏[1]‏ was a psychiatric hospital on the Oakley Farm Estate‏[2]‏ in Point Chevalier, Auckland, New Zealand. Built in 1865 on the Great North Road, it was one of the largest asylums in the Colony."