Nice score!
The body on those is HPL which stands for high pressure laminate. It's very much like Formica counter tops. The top is out of the same stuff too. I'm surprised to see that big of a hole in the side; that took an incredible impact to do that. I'm guessing the tyke went Pete Townsend/Paul Stanley on the poor thing.
The guitar will last much longer if you repair it and by that I mean just securing it so what damage is there doesn't enlarge. I'd remove all the strings, stick my hand in through the sound hole and gently push the parts smashed in back out so they were as flush as they could be. Then I'd take a small piece of plywood, the thinest you could find, and trim it so it's just bigger than the entire damaged area by about 1/2" or so and using wood glue I'd paint one side of the entire piece of plywood and then place that over the damaged area. If you have a nice, big, luthiers clamp you can clamp the plywood on to hold it while the glue dries. In lieu of a clamp, personally I'd find some suitable areas, at least 2 but not more than 3, where I could drive a screw into a pilot hole I would have drilled in the damaged portion of the side and let that draw the plywood up and hold it in place while the glue dries. You could leave the screws in or take them out after it dries and then put your sticker over it to cover the damage and the screws/holes.
If that sounds like too much then the next best thing would be a thick piece of cotton muslin, canvas really, and cut that into a sizeable patch that would fit over the damaged area. Once you've pushed out and made what you could flush, soak the canvas in hot water first, to shrink it, then soak it in a solution of 3 parts white or yellow wood glue to 1 part water. Pull it out, remove as much excess glue as you can and slip it inside over the damaged area. Set the guitar so that the patch uses gravity to stay in place while the glue dries. You could also do this with a fiberglass boat repair kit but it'll cost you some brain cells if you don't have respirator.
And it's messy.
If neither of those appeals to you, duct tape.
