Yes your dates are correct so she may be one of the eldest kids there but I have found alot these days that parents with kids born between Feb and April are keeping them back til the next year so its not uncommon for them to be turning 6 earlyish in the school year.

Council run kinders are usually 12- 15hrs a week broken up into smaller sessions, 3yrold varies I;ve seen some offer 5hrs week and some only 2.5hrs.

Childcare centres do offer kinder programs which if you need full day care you have that option there as council kinders are usually roughly 3hr days.