Need help to enroll son in a Sydney school

Hi all, I am really stressing about enrolling my 7 year old son in a primary school in Sydney.

I am applying for a study visa for Australia, but my son must be enrolled in school there before I can lodge my application. My studies begin at the end of February and the visa should take 3 weeks to process, so I need to have him enrolled by the end of this month.

I sent an e-mail to a school there explaining my situation, but I did not receive a reply. I think that is because the schools only open at the end of January, and so I do not know what to do.

Going alone to Australia and then applying for a school for him is not a personal option. Any advice would be really appreciated.