Yes you are missing quite a big something! I am genuinely interested in anything of this nature as I make a living setting up generators and non-grid supplies for events. What I think you have missed is that you are effectively installing the whole supply system rather than just connecting a consumers installation to an external supply system.
It is not a TT system, the inverter will be an isolated source or IT system. If you want to introduce an earth reference then you would be creating a TNS system. This is exactly the same as installing a generator.
The first letter T indicates that the source is solidly connected to earth, in the case of a single phase supply this is one of the poles which becomes a neutral once it is connected to earth, the letter I is used to indicate that the source is isolated from earth (or earthed through a deliberate impedance)
Why might you want a DP mcb? With neither pole connected to earth on a single phase supply then you do not have a neutral, just two lives. Depending on how your inverter is connected internally this could somehow be referenced to the case or it may be completely isolated from it (most likely). If the system is completely isolated from earth then I see no advantage to using a DP mcb in such a small setup, but if you are going to introduce an earth via a rod and then connect it to the 'earth' terminal of the inverter then you could end up with the two poles at different voltages relative to the earth and then need DP protection.
Without an earth reference connected to the inverter output then your earth rod and RCD will do absolutely nothing. Without an earth reference at the source then a current cannot flow to earth and so an RCD achieves nothing.
Personally I think you are over thinking a simple system and would be best just plugging in to the inverter with TRS and 4ways rather than over complicating it with rods and RCDs and suchlike as they could introduce more problems than they solve. Keep it as a simple inverter output which is isolated from earth.