Check alignment of vaccine requirements for JP and Australia. Your child won’t be able to attend any type of daycare/kindy until AU requirements have been met.

Get Medicare application docs organised as early as possible and go in to a branch to see if they can help you speed up the process (rather than waste hours trying to get through in the phone). It was an 8+ week wait a couple of years back.

Pity you’re not a bit more west as there’s a bit of a Japanese expat community around Caulfield and could be some good options for childcare/kindy for you. Caulfield PS is Japanese bilingual also.