I asked the same question on another forum last year. It is pretty slow over here so I will tell you what I was told.

Peony do not have deep roots so it should be easy to dig up. Try to get as much of the root and soil so it does not know it has been moved. Plant right away.

As I do all transplants if I am digging at a bad time I do not divide until the plant is strong enough to live through the move. I would not divide until it has grown in its new home for at least two growing seasons.

Peonies like a good chill in the winter. In order to set their flower buds, peony roots should be planted relatively close to the soil surface; only about 2-3 inches deep. It may feel odd to leave roots so exposed, but peonies actually need this chilling to attain dormancy and set buds.

Thanks for asking and answering this question. My two peonies aren't doing well at all. They are up against a wooden fence. I am going to transplant them in the fall. I didn't realize they could be transplanted so shallow.

Large old peonies are going to have large old roots. Peonies grow large storage roots that look like sweet potatoes. When dug up they are brittle and easily break off. Normally when you are going to dig and divide in the fall when no foliage is on the plant, it is recommended that after digging you let the roots lie on the ground for a day or two to cause the roots to relax and lose the brittleness before dividing. Digging in July I would not divide now but replant as is with as little root disturbance as possible. For most soil textures this will mean soaking a day or two before digging. I would not fertilize now and plan on digging and dividing in the fall. Doing this will result in the least loss and the most possible divisions. Although the top of the roots are very close to the soil surface, the roots themselves can easily be two or more feet deep. Al