There will be no TARDIS in New Eden. There will be no Doctor in this event. The closest thing is an item that drops in the sites.
Scale Model of a Blue Box
This peculiar rectangular cuboid appears to be a small scale model of a presumably larger object. The object is blue in color, with partially obscured textual markings near the top. The white text appear to be written in a common human script, but only the first and last letters remain legible: POL ----- OX.
Everything Doctor Who related will come from the anomaly we are traveling two, which is canonically in the Whoverse. We do not know how or why the Whoverse is ripping across the multiverse but if you have ever watched Doctor Who its pretty standard for an episodes premise