Does anyone know if it's possible for a child to be buried on the Chatham Islands around 1909 without the death being recorded on the mainland?

I have the birth data for Charles Roy Goyder Christie, b. 1909 Wellington, but no death seems to have been recorded. His brother, Charles Roy Martin Christie was born the following year. With the similarity of names, it seems likely that the first Charles Roy died before the birth of his brother.

Are there any records of burials on the Chatham Islands? I believe the Christie family were on the Islands around 1909-1914. Is anyone travelling there willing to check out the graveyards for Charles Roy Goyder Christie, please?