I have 2 IJ's and each is kept in a Boaphile (4' x 2' x 18"). They have a plastic tree thingy that is about 1' tall on the cool side and I made a shelf out of plastic office letter holders that is about 10" tall for the warm side. They both spend 95% of their time in either the tree or on the shelf. Pretty much the only time they are down and/or in a hide is after they eat or during a shed cycle.
You didn't mention which Carpet you are looking at but I can say that my IJ's would not be happy in a tub, IMO of course.