How to manage stock fulfilment from multiple warehouse locations?

I have stock in Warehouses in 3 different countries (Denmark, USA and Australia) but using only one website/domain.
If for example Australia runs out of stock for a certain SKU and don’t to be possible to order this SKU to Australia.

I’ve set up locations for the warehouses and shipping zones for each of them. However when testing, I can order a product that should be out of stock. In this case a product that is not in stock in Europe but it’s still showing the shipping rate for Europe when entering a shipping address for a European Country.

Any ideas what the problem might be? Thanks in advance