I can think of a couple of reasons I would not use peanuts.
1) Many of the peanuts today are water soluble, and very easy to dissolve
2) The way that the door holds its curve (unless you have or are adding something like a special web frame) is by the skins and core working together (in tension, I believe, although I'm not a physics expert). So the bond between the outer skin, the intact, dry core, and the inner skin is important. Peanuts would not have the integrity to perform this way.
So I would want to put in a sheet of core material, then bond the skin back on with epoxy, and then "tape" the seam (where the skin was cut) with fiberglass tape. I don't think peanuts would work well for this.
Coring material for boat decks is often made up of "blocks" of flat material held together by a scrim, so that they can make a curve but still stay together as one sheet. Or you could probably bend a solid sheet okay.
I would order a sheet of coring and proceed with the repair as if it were a boat deck. It comes as balsa wood, or foam (several varieties). Check to see what thickness you need when you have the door apart.
If your door curve is no longer what it should be, this is your chance to change it, as once laminate the new (old) skin back on, it should hold the curve you set it at.
Here are some examples from one retailer, but there are many:
As far as step by step instructions, the process would be very similar to that of re-coring a boat deck (except, lucky you, much much smaller and less labor intensive). Let me see if I can find a set of instructions online (I don't have time to write one out right now). I'll come back and add a link (or, feel free to ask specific questions).
Edited to add: Okay, maybe it's quicker just to write a synopsis of one way to go about it. This is just the basics and there could be more steps depending on what you find
1) Remove the door from the trailer and support it on a work bench. Then cut out the inside skin with a dremel, grinder, circular saw, etc.. You can either cut it so as to re-use it, or plan to lay up a new one. The fewer pieces you cut it into, the fewer seams you have to re-glass later.
2) Remove the rotten core (I think some Bolers had a full door coor and others just had some braces inside - I imagine there was a lot of variation, and probably some "punting.") If it's really rotten, it might just fall
out on its own; if it's only partially rotten you might need to use chisels and/or something like a Fein MultiMaster.
3) Clean up the insides of both skins by sanding.
4) Solvent wash the insides of both skins.
5) Does the door need to have it's curve adjusted? If so, now is the time. You could perhaps build a jig to hold the door in the desired curve while you work.
6) Cut core to fit and mark it for easy identification.
7) Assemble epoxy ingredients so you are ready.
8) Wet out inside of outer skin with neat epoxy
9) If you are using core that is divided into squares on a scrim, then fold them open backwards (like eating a mango that is cut) and force thickened epoxy into the gaps.
10) Lay down a layer of thickened epoxy on the inside of the outer skin
11) Lay core onto the epoxy and flatten it. Squeegee off excess epoxy. Let cure.
12) Remove any huge imperfections while it is in the green stage
13) Wash off amine blush with 3M pad and water
14) Sand fair then vacuum and wipe down with acetone
15) Coat with epoxy and then lay inner skin down on top of core (might add thickened epoxy too). Use gravity and heavy things to "clamp" while it cures (make sure outer skin is properly supported).
16) After that cures, then remove blush, sand, etc.
17 Add fiberglass tape and neat epoxy resin to cover cut line on inner skin. If you want it to be flush you can sand/grind recesses next to cut line.
18) Remove blush, fair, sand, acetone, paint
Note: I only had a few minutes and have surely missed some things, but this gives you the idea. If you google "deck re-core" you will find web pages and photos. Note that many people take shortcuts, or maybe don't exactly know what they are doing, etc. (people are just trying to do their best, but...).