Where can you apply for red card/green card (equivalent to site safety card in NZ) for a carpenter to work in Melbourne?

I think you can get a blue card online before you even arrive in Australia, try googling blue card online.

You can sit the test for this online before you even leave NZ, check out the Australian Master Builders website. It's called white/blue card which is a safety awareness training certificate that anyone must have before they can even step onto a building site of any kind. Here are some tips from a recent newspaper article. Contact Master Builders in Australia before leaving NZ, even if it's only a few weeks in advance. Go to where the work is - contact Master Builders for details of potential employers before leaving. Be prepared to put in some extra work in NZ to meet some of the Australian carpentry requirements. For example, being able to pitch a roof is an elective here, whereas in Australia it is a requirement, which means proof that the person can carry out the task is needed. So, if you contact Master Builders in advance it will no doubt save you lots of time and money. They can help get the ball rolling for you. Good Luck!