Assuming that it's a herbaceous peony that dies down each year, now is just about right (this is when you would divide them)
You should still have some foliage so you can see where the stems are. Cut back the foliage and then carefully work soil away from the stems to find the extent of the rootball. Prepare you new planting hole and then lift and transplant the peony. Don't plant it deeper than it already is.
Be prepared for it to sulk for a couple of years after the move.

Thanks very much. The peony has been stuck in a corner and totally obliterated by a hydrangea (and this year attacked by bindweed) so I’m sure it will thrive next year (?) I can be patient and wait for the flowers – have been for years now anyway. Once again, thanks for the advice.

I'm going to disagree, it should be moved as soon as all the top growth has turned brown. Paeonies start into growth below ground very early in the season so should be moved as soon as they go dormant. It is important that herbaceous paeonies are replanted with the growth bud AT SOIL LEVEL (not buried). There is no reason for it not to flower again next year - I moved 8 paeonies a few years ago, and all but one flowered the year after the move.