Welcome to the forum. This is a good place to talk about your difficulties.
Like Geoff I wonder why her has chosen this time to leave. You say he "tends to live in la la land" Does this have anything to do with his decision to leave? I find it strange that he has no income or other financial support but wants to leave. No need to answer if you prefer not. I see you wrote not much is changed which I presume means in your relationship.
It may b e a good idea to get some legal advice. The Women's Legal Service in your state may be able to help there. I understand you can have one or two free consultations so it's worthwhile checking out.
As Geoff has said, you can be living in the same home and still be classified and a separated couple. If he goes to CentreLink and applies for a benefit he will help both of you financial. For me that would be as far as I would go to help. I feel he must find somewhere to live by himself. Can he live with his parents and do they know about the separation? Selling your home is a huge step for you and your children. Can you talk about that with your husband?
How is all this affecting your children? Do they know your husband wants to leave? I think it will be hard on them to know their dad is leaving. If your husband is not working can he complete your home? As you say, it will be very difficult to sell a half built house and of course you will get very little for it and further stress to everyone's life.
How well do you get on with your in-laws? Again I wonder if they know he wants to separate. Can they support in some way. I know I am asking a lot of questions but I am at a loss with this one because of the circumstances.
Please look after yourself and post in here if it helps.