Strike a centerline on the back of the plaque and pre-drill two holes, counter-sinking so the screws will drive flush. Drive the screws so they just poke through the front of the plaque; use the screw tips to locate your deer head and center it. Pre-drill into the deer head. Coat mating surfaces in glue, then drive the screws home.
Mount the antlers with a spot of glue and a screw. If you want to hide the screws, plug the holes with a scrap of dowel.
Drill two holes in the plaque so you can mount it to the wall. Use some heavy-duty drywall anchors
so you can hang stuff on the antlers.