We introduce a two-stage robust optimization (RO) framework for the integrated planning of a drone-based disaster relief operations problem (DDROP). Given sets of demand points, candidate locations for establishing drone-supported relief facilities, facility types, drone types, and relief items types, our first-stage problem solves the following problems simultaneously: (i) a location problem that determines the number of facilities to establish and where to establish them, (ii) an inventory prepositioning problem that decides the quantity of relief items to store at each established facility, (iii) a fleet sizing problem that decides the number of drones to deploy, and (iv) an assignment problem that assigns drones to established facility and demand points. In the second stage, the model determines a relief distribution plan and enables the reassignment of drones to demand nodes. We equip the RO model with an uncertainty set that captures the relationship between facility disruptions, demand for relief items, drone operational status, and the remaining usable fraction of pre-positioned supplies after the disaster. Additionally, we explicitly model the dependency of post-disaster drone functionality on the pre-disaster assignment decisions. To address the challenges of integer recourse, we derive a K-adaptability approximation of the RO model and develop a column-and-constraint generation (C&CG) algorithm to solve it. Moreover, we introduce several strategies to enhance the computational performance of C&CG, including an efficient warm-starting mechanism, symmetry breaking constraints, and valid inequalities. We present extensive numerical experiments that demonstrate the computational efficiency of our framework and provide valuable insights.