what material would work for this?

DrewE wrote:
1/4" plywood (or even a bit thinner material) with some wood strips, say 1/2" x 1/2", glued on the back to stiffen it would work fine. Maybe have three such strips horizontally across the width and one vertically at each end to tie things together. It's a question of making the structure more rigid as much as making it stronger.

Another approach would be to build up a composite structure of thin plywood skins and rigid foam insulation board in the middle, all glued together. That can be incredibly strong for the weight. The stresses are carried by the plywood skins, and the foam serves to keep them flat and in alignment with each other.

For fastening to the wall, I'd consider using some decent-sized pieces of Velcro so the headboard is readily removable if that should be necessary for some reason, say because you're unfortunate enough to have the glass in the window get broken.

I was thinking about the Velcro as a good fastening option. I've learned the hard way (in home repair) not to assume that you will never need to get into anything. Another option would be to use the same #2 square-bit screws that are in everything else. They are small enough to be inconspicuous on a patterned fabric.

That's a good idea with the ribs on the thin material. I could put them in the area directly over the window, to take care of the slightly recessed depth of the window. Then the remainder of the headboard would be flush against the wall, no need for reinforcement there. I could just cut a few strips out of the same material as the main part of the headboard.