We address the challenge of learning to manipulate deformable objects with unknown dynamics. In non-rigid objects, the dynamics parameters define how they react to interactions -- how they stretch, bend, compress, and move -- and they are critical to determining the optimal actions to perform a manipulation task successfully. In other robotic domains, such as legged locomotion and in-hand rigid object manipulation, state-of-the-art approaches can handle unknown dynamics using Rapid Motor Adaptation (RMA). Through a supervised procedure in simulation that encodes each rigid object's dynamics, such as mass and position, these approaches learn a policy that conditions actions on a vector of latent dynamic parameters inferred from sequences of state-actions. However, in deformable object manipulation, the object's dynamics not only includes its mass and position, but also how the shape of the object changes. Our key insight is that the recent ground-truth particle positions of a deformable object in simulation capture changes in the object's shape, making it possible to extend RMA to deformable object manipulation. This key insight allows us to develop RAPiD, a two-phase method that learns to perform real-robot deformable object mobile manipulation by: 1) learning a visuomotor policy conditioned on the object's dynamics embedding, which is encoded from the object's privileged information in simulation, such as its mass and ground-truth particle positions, and 2) learning to infer this embedding using non-privileged information instead, such as robot visual observations and actions, so that the learned policy can transfer to the real world. On a mobile manipulator with 22 degrees of freedom, RAPiD enables over 80%+ success rates across two vision-based deformable object mobile manipulation tasks in the real world, under various object dynamics, categories, and instances.