The task of inductive link prediction in knowledge graphs (KGs) generally focuses on test predictions with solely new nodes but not both new nodes and new relation types. In this work, we formally define the concept of double permutation-equivariant representations that are equivariant to permutations of both node identities and edge relation types. We then show how double-equivariant architectures are able to self-supervise pre-train on distinct KG domains and zero-shot predict links on a new KG domain (with completely new entities and new relation types). We also introduce the concept of distributionally double equivariant positional embeddings designed to perform the same task. Finally, we empirically demonstrate the capability of the proposed models against baselines on a set of novel real-world benchmarks. More interestingly, we show that self-supervised pre-training on more KG domains increases the zero-shot ability of our model to predict on new relation types over new entities on unseen KG domains.