Well a replica has at any rate and they are busy putting it together in the grounds of the Royal Hospital Kilmainham at the moment. I went in to the royal Hospital this afternoon and took some snaps - this thing really is enormous.
We've got it for the next month or two because NASA, ESA and the CSA are holding a technical review of the JWST at the Royal Hospital from June 11th to June 14th. John Mather, the JWST Chief Project Scientist, will give two public lectures while in Dublin. Gizmodo of all places has a neat little write up, some older pics of the model and a video.
I can't find all the details but there is more information and (free) booking details for the lecture on Tuesday next in Trinity at the Royal Irish Academy website http://www.ria.ie/committees/chemicalandphysicalsciences/new.html
-(edit: given that it's on next Tuesday it is now booked out ).
For any XKCD fans in the audience John Mather got a Nobel prize for COBE so he is basically ultimately responsible for this: