Not sure what is going on with your peony. Water when soil is dry several inches down. Saturated soil will kill the roots, resulting in wilting. It could also be transplant shock. Hopefully you used a well-draining, commercial and sterile potting soil for the container because native soil compacts too much and the plant was planted at the same level as its original container. The other problem may be that this specific cultivar does better in cool climates and will not adapt to Southern California’s mild weather conditions. Suggest you go to the nursery where you purchased it to find out. Other tips: Peonies like soil high in humus or organic material, mulch to mitigate soil temperatures and water levels and provide afternoon shade if the weather turns hot and dry. Peonies need to be planted fairly shallowly, or they will not bloom. Also check out online resources to grow peonies in southern California such as: ilovepeonies.com
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It looks like an open head formed, water got in the bud and botrytis has taken hold and is traveling down the stem. It needs to be cut off below the lowest damaged spot and the remains removed and destroyed, not composted or left around the plant as it will just spore out and infect others. Botrytis is a pervasive disease found everyplace though there are strains specific to peonies.