Raising the bathroom floor

I'm considering DIY'ing a new bathroom, and that will include raising the bathroom floor by ~9inches so it's level with the hall. I'm in the early planning stages and will probably take some time off work in October to do the bulk of it.

How would you go about doing this? I'm aware of the building regs on joist spacing etc. and happy to work all that out, it's just how to get to that point I'm not sure on. E.g., do I use posts like when building a raised decking, and if so how do I determine the size? Stripping back to the old floor seems the most correct way, but can I take the slightly lazier option of building on top of the old subfloor?