Are you ever going to remove the skull from the plaque? If not, I would try to run a pilot hole with a drill through the hinge of the jaw (where it would law on the wood plaque) into the socket of the head. I would then glue this juncture. After that, I would pilot the hole once again through the bottom side of the plaque, and again through the joint of the jaw, and then countersink a hole in the bottom of the plaque, and drill a 2 or 3 inch wood screw, or whatever size it takes to hold the skull in place without being too deep or too shallow. I've glued a deer skull to its jaw set and it held, so by adding a wood screw to hold the jaw and skull together plus the skull and jaw to the plaque, I think that would definitely support it enough to hold.
There's several ways to accomplish the end result I'm sure, but this is what I would try if it was me. You will probably come up with an alternative method.