Not too early at all. The idea is preposterous and silly. With superman being a super human, he possesses flight at incredible speeds and tremendous hearing..and if Gotham is right next to metropolis then there is essentially nothing batman is needed for, when supes could take care of it instantly. I don't know, just my opinion. I realize that we have no geographical whereabouts to where these fictional cities have been in the past, but I'd like to think it was more of an east coast, west coast thing. Could superman still take care of crime in Gotham then? Of course but it would be a Herculean task and thus makes more sense for batman to control his section.
And yes I was well aware that there was kryptonite in the trailer but that does not mean that his suit is laced with it. Is it possible? Yes, but it's purely just speculation at the moment.