Well, first and foremost, it is going to be a British Protectorate, as a matter of course as well as of neccesity. This probably means that there will be British forts dotting the land, especially in the beginning, until *Indiana (for lack of a better name) developes its own standing army. The first few decades of this nation are actually going to be fascinating as it struggles to form it's own identity and institutions. One of the biggest factors at play is going to be integrating the different tribes together: remember that a Pan-Native identity didn't really exist at this time, and that not all of the peoples included in the borders you established, supported Techumsah and his movement.
I suspect that it will begin very much as a Confederation in spirit. There will be a central government (I imagine Prophetstown will be the capitol) but there will also be a lot of local autonomy which the member tribes able to conduct internal affairs as they are used to, but with the national government overseeing foreign affairs, trade and the like. This isn't too different from over Native Confederations over the years, actually - the Anishinaabe operated very similarly. However, this central government will have more powers than such councils had in previoud Confederations. Once again, this will be partially as a result of a strong personality like Techumsah being it's Founding Father, but also by neccessity - the US is still going to be breathing down the new nation's neck, and Britain is going to want a stronger central government that it can deal with. Most likely there is a central Council, and each member tribe appoints a certain number of representatives to sit on it. This will, in time, probably evolve along the model of the British Parliament.
Also, the internal dynamics caused by the different tribal groups is going to be interesting. Are they assigned territorial boundaries, ala States or Provinces, or are they viewed more as cultural and ethnic groups (an Ojibwe would follow Ojibwe customs and laws, and vote in Ojibwe elections, whether he lived in *Duluth or moved to *Detroit). Also, what mechanisms and powers would the central government have to mediate disagreements between its individual members.
Britain is certainly going to appoint an ambassador, but just how tightly Indiana is tied to Britain is going to determine whether they have a Governor-General or not.
I also wonder what the rights and status of whites will be in the Confederation. There will be no practical way to ban them entirely, though some way want to - during the first years, the Fur Trade will continue to be an important source of income for many of the member tribes, after all, and those British soldiers are too important for defensively and economically. Furthermore, Britain would not turn a blind eye to such a thing. And so they are going to have to find a way deal with them, while also not being so inviting that the native population gets swamped by settlers surging into the land.
Honestly, this is one of those great topics that don't get explored on the Boards nearly as much as it should. These are jsut some of my random stream of conciousness thoughts, and I'd be really interested in hearing what others have to say