Peonies should be transplanted in the fall before the first expected frost. They may not bloom the first year after transplanting because the roots need time to establish.
To transplant a peony, cut the plant back to 3 inches above the ground. Use a handheld garden shovel to dig around and under the plant. Lift it out of the dirt and set it aside. Dig a hole in the new spot large enough to accommodate the root ball. Mix some compost in the soil to give the root ball nutrients. Spread the roots out a little if they are compacted, and set the peony in the hole. Pack the soil removed from the hole around the plant, and water deeply for about five minutes.