Dividing a peony is not required to keep the plant blooming. If you are moving a peony that has been in the ground for years the root system may well be too big for you to dig and move without a backhoe. As you dig you can divide as you go to reduce the mass to a manageable size. You will no doubt lose some of the root no matter how careful you are. If your peony is less than five years in the ground moving in one piece should be quite possible. Al