Dig it in the fall. Depending on how old it is it may have a very large root so start your digging about 18 inches away from the plant. You may want to divide it before replanting, depending on what the root looks like. I would not mulch over a peony root. Al

(Posed on another question) We have found that a lot of time, it is not the act of re-potting, but the material you use to re-pot that prompts the newly enthusiastic blooming. Most blooming plants need phosphorus to produce blooms. We recently moved into a house that had beautiful gardenia bushes in front. The previous owners said they never had really bloomed very much, maybe a dozen or so each season, but they were nice when they did. I started a regiment of high phosphorus fertilizer (10-50-10) in the winter and through the spring. I am thrilled to say that we ended up with about 500 blooms on 10 feet of bushes this spring. They have been spectacular. The entire neighborhood smells wonderful these days. Best of luck!