Cut a circle with a 2-foot diameter out of a sheet of 3/4-inch plywood using a jigsaw.
Cut the circle into four equal quarters. You will use two of these, and the other two can be saved for another shelf.
Cut a 1-by-3-foot rectangular shelf out of the same plywood. Round two of the corners with a jigsaw along a 3-foot side. This will be the front side.
Measure in 6 inches on one side of the shelf and make three pencil marks, spaced out evenly along the 1-foot thickness. Do the same on the other side of the shelf.
Drill 1/16-inch pilot holes through the six pencil marks.
Place a quarter-circle over each line of holes, with the rounded edges facing the front of the shelf.
Nail the shelf to the quarter-circle supports with 5d finishing nails, hammered through the pilot holes in the shelf's surface and into the top edge of the supports.
Cut a 24-inch piece of 2-by-2-inch board. Place it onto the rear edge of the shelf's underside, between the two supports.
Nail the board to the shelf with more 5d finishing nails, hammered through the shelf surface and into the board every 4 inches.
Drill two 1/8-inch holes through the 2-by-4-inch board, spaced 18 inches apart, going from the front to the back. These holes will be used to mount the shelf to the wall.
Sand the wood with 120-grit sandpaper to remove splinters and rough areas.
Brush on a coat of primer and allow it to dry for the time recommended on the can.
Brush on a coat of paint and allow it to dry. Use colors that your child will enjoy.
Use a stud finder to locate two wall studs within the wall. Mark their locations with a pencil.
Drill a 1/8-inch pilot hole into each wall stud, positioned horizontally at an easy height for your child to reach.
Screw the shelf to the wall with two 3-inch wood screws, passed through the holes in the 2-by-4-inch board and into the wall studs.