I think you are in pretty much the same situation as everyone else. You just need to think about what you need to work as an ordered development and the documentation needs will become apparent. This was nearly always the case when I was a consultant because the clients are generally non-technical marketing folk who really don't know what they want. You have to lead them by the hand.

We always used to start with a Product Specification that described what the product was supposed to do and how well it should do it i.e. function and performance. It does not matter that this is incomplete but it does matter that all sections are present (even those not yet defined) as it serves to show the client what you need to know to complete the job. Then we did what we called a Feasibility Study but its purpose was basically to work out how we would do the design and to flesh out the Product Specification. We would often put crude software together as part of this to show the client (much like your version 0.1). Only once this was done did detailed design begin and by then most things were pretty much tied down.

Ian