There are some websites by occupational therapits and speech pathologists who have come up with check-lists for getting kids school ready.

My daughter used to go to preschool for 3 hours a day 3 days a week. She started when she was 3. We increased it to 4 days when she turned 4, and to 5 days when she was 5. That way, by the time she started kindergarten and had to stay 6 hours at school, she was quite prepared. They were longer days but she loved it and we didn’t have any drama.
You can look in Internet for information and tips. I think this website could be quite helpful: http://www.schoolatoz.nsw.edu.au/wellbeing/development/starting-kindergarten-soon