For general information, I am just now in the process of digging peonies from nursery beds for replanting, which activity will (I hope) be followed by planting seedlings into the holes left in the nursery beds, or into whole new nursery beds.
This is the time of year during which, in temperate northern hemisphere areas, peonies are best transplanted if the transplant will disturb the root mass (which pretty much covers most peonies except the small and immature, or those grown in large pots with a proper soil). The reason for this timing being preferred is that the plants start to grow new feeder roots with cooler ground temperatures and autumn rains. These feeder roots will continue to develop and feed the main root during the rest of autumn, much of winter, and through spring until the ground becomes too warm. Peonies transplanted in spring thus have a much shorter period during which to develop the feeder roots, which results in a poor start for the spring planted peonies.