Put your name down early. 5 wks preg is a good time. where I work, this *might* get you in before the baby is 18 months old.
Call before you go and look anywhere (or if you don't, don't get annoyed when nobody is available to show you around)
DO NOT cry, beg or try bribery. It is a waste of yours and the Centre's time.
There are loads of good places in Sydney's Inner West, but not a great deal of availability. You may have to settle for something second best if you don't already have your name down.

Just telling it like it is.