If I were to do a model of the building, the first thing I'd do is try to get a good set of plans/drawings... it takes a lot of the guesswork out, and helps make sure everything ends up in proportion.
The structure seems to have three main components:
* Walls: I would look at using foam core (styrofoam laminated between two pieces of cardboard; it's sold in sheets and it's also sometimes used to make those booths used for science fair projects). If that's not available, I would go for plain styrene, or if that's too expensive, cardboard.
* Dome: Your best bet is probably to find a ball of similar desired radius, and then cut away part of it to make the dome. The mesh and plaster route could work too, though I would try to adapt a strainer/sieve rather than try to form a curved structure from a flat piece of mesh.
* Columns: I would start with with dowels or plastic tubes.
In general, try to get the overall shape first. Save the nitty gritty details (column pedestals and tops, engravings, etc) for the end. That way you don't end up with highly detailed columns and nothing else.