The potential for Planck to detect clusters of dusty, star-forming galaxies at z > 1 is tested by examining the Herschel-SPIRE images of Planck Early Release Compact Source Catalog sources lying in fields observed by the Herschel Multitiered Extragalactic Survey. Of the 16 Planck sources that lie in the ˜90 sq. deg. examined, we find that 12 are associated with single bright Herschel sources. The remaining four are associated with overdensities of Herschel sources, making them candidate clusters of dusty, star-forming galaxies. We use complementary optical/near-IR data for these `clumps' to test this idea, and find evidence for the presence of galaxy clusters in all four cases. We use photometric redshifts and red sequence galaxies to estimate the redshifts of these clusters, finding that they range from 0.8 to 2.3. These redshifts imply that the Herschel sources in these clusters, which contribute to the detected Planck flux, are forming stars very rapidly, with typical total cluster star formation rates >1000 M⊙ yr-1. The high-redshift clusters discovered in these observations are used to constrain the epoch of cluster galaxy formation, finding that the galaxies in our clusters are 1-1.5 Gyr old at z ˜ 1-2. Prospects for the discovery of further clusters of dusty galaxies are discussed, using not only all sky Planck surveys, but also deeper, smaller area, Herschel surveys.