Moving peonies in April in Idaho (zone 5-6) with shoots already emerging is risky but doable if you must. They likely won't bloom this year.
If you can wait until September, do it then—fall is ideal for peony transplanting.
Emergency Transplanting of Peonies After Disaster: Temporary Potting and Replanting
Transplanting Established Muscadine Grape Vine
Growing Peonies in Containers: Pot Size, Transplant Shock, and Bloom Recovery
Moving Overgrown Mums: Timing and Technique for Minimal Shock
Transplant Shock in Iris: Don't Cut Green Leaves—They're Feeding Rhizomes
Transplanting a Mature Clematis Near Green Bay, WI (Zone 5)
Moving Blooming Iris in June: Minimizing Shock for a 100-Mile Journey
Summer Transplanting Bulbs and Roses in Iowa Heat
Large Perennial Bed Renovation: Saving Peonies Amid Weeds
Transplanting Lilacs in Prince George, BC with -5°C Nights
Transplanting Mature Hollies in Summer: High Risk, Better to Wait
Transplanting Texas Sage in Central Texas: Timing and Technique
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