you don\'t need to have health exam or police check until you are told.
by the way, just want to remind you even though you pass the skill assessment but not necessary mean you are automatically registered as GP. it is 2 separated process.
assume you have enough points and there is no queue for your occupation, you should receive application soon after EOI submitted. then the whole process usually took around 3 months to complete.
as said, you can only do health check and police certificate when they issue a letter asking you to do so.