I've never actually dug a 2'X2' hole for any of my peonies but I plant in raised beds because the soil in my garden area is hard clay. If your peony has been in place for quite a while the rootball might be about that big anyway! Are you planning to divide it before replanting? Do you have good soil where you're planting?

Mulch a spot like crazy right now. A foot deep. Wait as late as possible to transplant, then loosen the soil as deep as possible, dig a small trench, put in the peony roots, and cover them with heavily composted soil to an inch deep. Then add another foot of loose mulch on top until spring.