I think your peony will be fine. I've had to move them in spring after a lot of growth and the plant wilted for a short period then started growing again. I'm in a much colder zone than you're in but you putting one in the ground in March should be comparable to me moving one in May/June....Just make sure you don't plant it too deep. You'll probably get a response from one of the CA members, too! Good luck and enjoy your peony!

I am sorry to hear that this happened to your peony. It would help the peony a lot if you can provide it with some shade and mulch at this time while it is under stress esp. if the weather is hot where you are. Liz is right - your peony will be fine provided that it does not get wet feet where you plant it.

You don't have to worry about planting potted peonies,
the roots aren't disturbed, so they can be planted any time. Only transplanting has to be done in the fall.
Planting in March, lucky you!! Still snow here!

Where you live you can plant your peonies anytime. Your main concern should be lack of sufficient winter chilling. Your buds should always be visible, not buried, as you will need to get your winter chilling from air temperature as your soil temperature will not be cold enough. Your peony will grow lots of foliage, just no flowers. Pick the sunniest spot in your garden for your peony. Al