Are you in Australia? Or just planning ahead?

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Start with:

http://www.theatre.asn.au/book_page/coming_from_overseas_where_to_start

I would also add that most playwrights in Australia both do not earn a living in general from their work, and find it difficult to either publish or stage their plays without considerable funding and/or winning awards. Whilst playwrights do see their work staged in small fringe productions and at the local amateur group, it's highly unlikely to be successful and a backup plan would be needed.

I can't think off the top of my head any specific playwrighting courses, but try the obvious: NIDA in Sydney, WAAPA in Perth and VCA in Melbourne. Playwrighting is often covered, in lesser extent, in other theatre courses, as well as creative writing courses around the country.

As an actor, you will have just as much a hard time, unless you have a considerable amount of training and experience already.

If you haven't thought about it already, you'll need a backup plan for earning money if you plan on coming.

Jellyfish shadow puppet for sale at
Puppets in Melbourne