Paint the rock with gesso and then brown paint, letting it dry between coats. Cut out ears from brown felt and inner ears from cream felt. Cut a pair of antlers from craft foam. Cut 1/3 off the bottom of a red pom pom to create a flat surface. Glue everything together.
White glue is plenty strong to hold felt and craft foam to a painted rock, but the pieces do need some support while they're drying so that they don't slump. I found that a camera battery was the perfect size to support the antlers until the glue was dry.
I'm thinking that my next Pet Rock will be an owl, though I reserve the right to change my mind.