I think if you can keep the clump as intact as you can, you will be as likely to see blooms this spring as you would have if not moving. Before they start any growth is the best time. I have planted bare root in the spring & gotten some weak blooms, sounds like your roots "should" be mature enough to bloom & with some luck, moving won't delay that.

Due to sad circumstances, I had to move my peonies last Spring while they were in bud, after just moving them there the previous Fall. Here's the advice a professional gardening friend gave me:

Soak the peonies; dig big root ball - packing the dirt toward the plant center with shovel as you dig. Put into large pot or burlap. Replant as soon as possible. Put compost into the new hole. (prep the new area as early as possible with compost) She also recommended shading the plants during midday for awhile after the transplant.

I moved 3 budding peonies at the end of May, and the two older plants came to full bloom in June!! It perked me right up!

And, yes, the earlier you can move them, the better.