I would be quite concerned about the attachment points for engine bearers, wings and struts etc. The internal structure you (i assume) are trying to replicate is somewhat different to a conventional modern aircraft. If you are attempting to make the interior look similar at least in the cockpit areas, how would you achieve the appearance of interior ply (or strip layups) , longerons etc while maintaining the necessary fillets required by glass/fibre construction?
Carbon fibre is an alternative to ply that would require significant re-engineering of a very functional construction method, the weight difference as stated by Jan will likely be negligable at best, the cost would very probably be somewhat higher as you would need many of the more expensive timber working tools just to create the molds and frames etc in the first place and then add to this the vacumn systems etc
Using a secondary layer over ply can (structurally speaking) also be pretty redundant depending on the design. The fail/weak points of the original structure still exist, albeit now hidden by an outer coat/surface, and the dissimilar properties of the ply and secondary layer open other possibilities for structural issues.
Me personally, I'd hate the idea of buggering around fitting ply frames etc inside a molded skin only to end up with a featureless smooth exterior. No nail lines, no scarf joints, no bulges or ripples, drips of varnish, bloodstains (mine), etc...really, its all the interesting aspects of a ww1 plane gone...