Now is an excellent time to move them. The following was taken from the Iowa State University website.

Transplanting and Dividing Peonies
Peonies can be leftundisturbed for many years. Sometimes, however, it becomesnecessary to move established peonies. Peonies shaded by largetrees or shrubs bloom poorly and should be moved to a sunny site.Large, old plants may become overcrowded and flower poorly. Large,old plants should be dug, divided, and transplanted to improveperformance. The best time to move or divide peonies is September.
Moving established plants is a simple procedure. Cut thepeony stems near ground level in September. Then carefully digaround and under the plant. Try to retain as much of the rootsystem as possible. Promptly plant the peony in a sunny, well-drained site.

Division of large peony clumps requires a few additionalsteps. After digging up the peony, shake gently to remove loosesoil from the root system. Divide the clump into sections, makingsure each division has at least 3 to 5 eyes (buds) and a goodportion of the root system.

Peonies grow best in full sunlight and well-drained soils.Dig a hole large enough for the entire root system. Place thepeony plant in the hole so the eyes are 1 to 2 inches below thesoil surface. (Peonies planted deeper than 2 inches often fail tobloom satisfactorily.) Fill the hole with soil, firming the soilas you backfill, then water thoroughly. Space plants about 3 to 4feet apart. Apply a 2 to 3 inch layer of mulch in late fall.Straw is an excellent mulch. Mulching will prevent repeatedfreezing and thawing of the soil that could damage the plants.Remove the mulch in early spring before growth begins.

Transplanted peonies will not bloom well the first spring.They should be back to full flower production by the third orfourth year.

This article originally appeared in the August 11, 1993 issue, p. 134.