Yes. It being 3 years old, I don't know what it's root spread is likely to be. I have actually never moved one, just planted new ones.

Once the winter buds are set on the root crown in September these plants can even be divided, while the by then quite mature tops are still present. This is when a peony nursery near me here in the neighborhood used to lift and divide every year, cutting the still green tops off in the process.

So if it were me I'd just wait until then, when the plants will not be bothered by being handled.

I have to disagree with September although that is when most gardeners are told to move plants. Most growers start digging in about the second week of August. Since the bloom buds for next season if any are already established although not actively growing if you have time in August transplant then.

Edited to add that as long as a peony receives light from directly overhead they will bloom. There really are only a few that need the yellow part of the sun's rays to bloom.

If you were to move it now, the buds might not open so no blooms.

You could leave it, let it flower and enjoy the show, then move it after it flowers.

And it would most likely be fine and work on establishing itself as long as it is watered and cared for over the summer, and flower again next year depending how well/carefully you dig it up and move it.

I have done this a couple of times with an old peony I have and it has always bloomed and transplanted okay.

New roots come out during or after setting of winter buds late in the season, there won't be much "establishing itself" before then.