It does look like each panel is the same as the other one, so pictures of each and an overlay should have you all set.
But it also looks like each panel by itself is left/right symmetric. So a single picture, split down the middle, then the good side mirrored would also get you a replacement file.
You can of course step one further than repair.
With basic repair you can attempt to just cut the missing piece, and then wood glue to attach it in place without ever messing with the rest of the panel. If you want to preserve as much of the overall piece as 100% authentic, this is the route you should certainly take.
But, if you don’t care about it remaining flawless to the day it was made, and instead just appreciate the beauty… rip out the current panels (carefully!), and set new ones cut in a single piece in their place. But design some method of being able to easily swap out the panels, and then go wild and create as many custom panels as you want to swap out on a whim (can make seasonal ones, or special messages for events like graduations and birthdays…).
As for how you can design the easy swap… I would need to see the piece in more detail to have ideas that actually work. If the doors are thick enough, I would propose to cut a hollow section above the panel where you can slide it in and up, then let gravity pull down to rest in the bottom section. Snap on the outer scrollwork to hide the loose fittings required for such a mechanism.
Oh, you almost certainly need to contour the pieces after you cut them. You will have squared off corners straight out of the glowforge.
The ideal tool there is a router table. Lacking that, there are dremel heads that serve the same function (and full adapters to make a table too. Advisable, since using them without the table requires some experience and a steady hand).