Paged.
When we moved to Melbourne from Brisbane in September last year we got caught out. We'd planned on me looking after our two girls (4 and 11 months at the time) full time, but found we had to send kid #1 to Kinder prior to primary school. While that wasn't in the semi FIRE budget we live on we made it work. Our childcare centre has a government approved kinder program, so we get a 55% subsidy under the new system that started July 1st from the government, which reduces the costs of $127 a day down a bit. So as the local childcare (350m away) had kinder we sent kid #1 to it two days a week (which was their minimum allowable number of days) for childcare to guarantee her kinder spot. We still only go for two days a week to meet the 15hrs a week required of the kinder program and she's home with me and kid #2 the rest of the time.
Centrelink pays the subsidy straight to the childcare centre. And up to date vaccines are required, so if you have anything in writing from the Canadian government, you'll need to provide it. Medicare has a record of vaccines given in Australia, so using the MyGov website linked it directly to Centrelink for us.
When you say south east, inner 10km, or further out? North or south of the M1? We're in Preston, a couple of sisters live nearby us and I have a brother out at Narre Warren.