We propose a method for learning de-identified prosody representations from raw audio using a contrastive self-supervised signal. Whereas prior work has relied on conditioning models with bottlenecks, we introduce a set of inductive biases that exploit the natural structure of prosody to minimize timbral information and decouple prosody from speaker representations. Despite aggressive downsampling of the input and having no access to linguistic information, our model performs comparably to state-of-the-art speech representations on DAMMP, a new benchmark we introduce for spoken language understanding. We use minimum description length probing to show that our representations have selectively learned the subcomponents of non-timbral prosody, and that the product quantizer naturally disentangles them without using bottlenecks. We derive an information-theoretic definition of speech de-identifiability and use it to demonstrate that our prosody representations are less identifiable than the other speech representations.