Indoor robots rely on depth to perform tasks like navigation or obstacle detection, and single-image depth estimation is widely used to assist perception. Most indoor single-image depth prediction focuses less on model generalizability to unseen datasets, concerned with in-the-wild robustness for system deployment. This work leverages gradient-based meta-learning to gain higher generalizability on zero-shot cross-dataset inference. Unlike the most-studied meta-learning of image classification associated with explicit class labels, no explicit task boundaries exist for continuous depth values tied to highly varying indoor environments regarding object arrangement and scene composition. We propose fine-grained task that treats each RGB-D mini-batch as a task in our meta-learning formulation. We first show that our method on limited data induces a much better prior (max 27.8% in RMSE). Then, finetuning on meta-learned initialization consistently outperforms baselines without the meta approach. Aiming at generalization, we propose zero-shot cross-dataset protocols and validate higher generalizability induced by our meta-initialization, as a simple and useful plugin to many existing depth estimation methods. The work at the intersection of depth and meta-learning potentially drives both research to step closer to practical robotic and machine perception usage.