@utopia,
because workcover approved you for a 14 day private hospital stay, they should be able to find you a bed in a different private hospital. The public psych hospital system is always full to over-flowing, so I doubt they will try and get you into a public hospital. Just sit tight. The worst they can do is keep you in an emergency bed over-night. That's Ok, you still get to see a doctor there and you still get to be safe and well-fed. I know it's not ideal, but at least you are away from that dreadful psychiatrist!
He sounds like a real piece of work!! Wow, he really over-reacted to you wanting to not see him for a day. His actions seem extreme. Why discharge you from hospital just because of that? He must have had to deal with people who were way more challenging than you, in his career, I would think? Incredible.
Sit tight, @utopia. Just expalin what happened in as calm a manner as you can, and ask them to find you a bed elsewhere. There should be plenty of beds in Melbourne.