No reason why you can't do that, just remember to keep them watered and preferably in the shade, they are not bulbs after all. If they are old plants, I would not take the whole thing. You can actually take a size able division without digging up the whole plant and still maintain your established garden for the new owners. Al

Yes you can. Just pot them up now and keep them shaded more than you'd normally do peonies and plant them this fall. Make sure you add some sand or something to keep it we'll draining to the potting mix. I assume your peonies are past blooming now, right? Cut off the seed heads and try to get as much of the root as possible and don't disturb it if you don't have to. I'd wait until fall to divide if you can. If you can't, cut back all of the foliage as well as the seed heads. Good luck!