You might have a herbaceous peony now. Japanese tree peonies are grafted on herbaceous peony roots. If it dies back to the ground and then resprouts from the roots ... well, you can imagine.

If you have to take it, and still want to take it, dig it up with as much root as you can, wrap it in something like burlap and as much soil on the roots as you can manage, then plant it as soon as possible. Just heel it into a trench in the ground if you won't be able to plant for a while.

My recommendation is to order a nice new one for delivery this autumn. You'll be guaranteed a tree peony, you won't be stressed by the move, the plant won't be stressed by the move, and you should get flowers in the spring :)

Thanks, I think that's probably good advice -- although it feels a bit like abandoning a pet....