The school year is divided in 4 Terms, starting with Term 1 at the beginning of the year (see e.g. SA)
The different State Governments provide helpful information about their education system.
There is no mandatory 'Kindy' as in Switzerland before school. A lot of children stay in childcare until they start school, some go to 'Preschool' or 'Kindy' or called similar at the age of 4 and there are some children who have never been cared for outside of home before starting their first year at school. Also Kindy or Preschool can be run by Government, private or community providers and as with schools, you don't necessarily go the one closest to you. This is quite confusing coming from Switzerland, thus talk to other parents and check out the states websites (as e.g. SA).
German English bilingual schools are in Sydney and Melbourne. Adelaide has a School of the German Language teaching German only a part-time basis on Saturday mornings, the same applies for the German Language School in Canberra (Saturday Mornings, Monday Afternoons) and the Brisbane German Language School (Saturday Mornings).
Tip: If you know in which area you will be living and to which school you might send them, enrol your children from back home. Public Schools are zoned, that means children living in the school zone have priority in getting a place. Private Schools often have a waiting list, thus it pays to put your child's name down. The fees for private schools in e.g. SA range between $1‘200 and $12‘000 yearly and can increase to $23'000 AUD in secondary school.
CSA Oceania, the council of the Swiss abroad delegates for the Oceania region have a website! Created in October 2016 to improve information exchange and be present as delegates online.