the reason i suggested celotex is because i personally just happened to have it, and i've used it before for making the backing of a "rough in" mold before. you can get it at building supply places like home depot possibly - it's hard sheet insulation - something that would work the same is once it dries, expanding foam. it's about the same consistancy, and is super easy to model with a razor or exact-o-knife. in fact, almost any knife goes thru it like butter, making it ideal for shaping as you desire. the latex you can find at hobby stores, not sure what's in your area so it's hard for me to say
http://www.artmolds.com/gateway/studio/catalog/kits/latex_mold.htm
you can get latex from these people. doing this method will get you "in the ballpark" to having your exact mirrored piece.... depending on how much time/effort you put into making the backing.... and how elaborate the origional piece is. just remember, if there are any recesses, etc in the door panel (like handholds, or handles) you'll have to fill them in with modeling clay before pouring the latex, so the eventual cast will be able to have the finished product pulled from it (also so you can reverse the latex mold). then you can cut thru the area where the clay was when finished. to answer your question, yes - i've done something similar to this before, but not as big as an entire door panel. getting the latex on smoothly is something you want to do, but not too terribly important if when you reverse it, and make your inverted piece, if you put all the finishing touches on the reversed piece (basically, the first reversed door panel you make out of the latex mold). make that first piece quickly, and thick, so that you can sand/cut/groove/shape it to the way you want the finished product to look, then you can make yourself a more permanent casting from plaster and use it to create a near perfect mold to make your panel(s) from. parts release easily from plaster, and i've made pieces that are impossible to tell from the origional with them -- the detail is nearly 100% perfectly transfered with a plaster cast, so any imperfection in your door panel will be copied into it. also, remember the latex mold will not be perfect on the "reversed" side - especially on any edges that are particularly sharp. that's why i suggest making your first door panel from it just as a piece to use to make your plaster (permanent) mold. you could even make that first panel simply out of resin (to make it a bit easier to shape) since you'll only be using it to make your permanent plaster mold from.