Proper time is in the fall, but before I knew that I dug some up right after blooming one spring, divided & replanted. They bloomed next spring just fine. I would certainly plant them, just be sure not to plant very deep, only cover with an inch or so of soil. I imagine these haven't much growth yet? And assuming these are not tree peonies which have to be planted deeper. You are very unlikely to get bloom this year of course.
As far as holding overnight in water, I wouldn't think it necessary. I don't think it will actually hurt just overnight, but wouldn't leave them more than that. Lucky you to be getting peonies!

You don't say how much foliage the peonies have, which will wilt pretty fast. As far as dividing is concerned it is easier to divide if the roots are a little wilted as they are not so brittle and can be handled without them breaking where not intended. After planting you may consider providing a little shade until the roots pump some moisture into the foliage. Al