Bazzateer is on the right track, but a similar technique I've used is to make a sandwich panel with plywood glued to rigid foam. Very light, very strong and insulated. Use 2" rigid foam, glue it with a construction adhesive that won't melt it! Read the label. Spread as evenly as you can quickly, "clamp" it with weights. Glue up one plywood sheet at a time; you won't have time to spread the adhesive on both. Then, build a 2x4 frame around it to provide solid places for hinges and latches. Such panels are manufactured for use as a complete wall or roof - Homasote (check spelling) is a brand I've heard of. Check their website for ideas on how to best make a door of it.
I've made panels like this of 1/2" rigid foam sandwiched with 1/8" plywood-amazingly strong for its weight.
I believe rigid foam's R value is greater than fiberglass batts for equivalent thickness, but that's easily checked on the Web. Batts don't add any strength, though. With the rigid foam, I think you could use 3/8", perhaps even 1/4" plywood and have a really sturdy door.