This letter presents a new method to automatically transport objects with mobile robots via non-prehensile actions. Our proposed approach utilizes a pair of nonholonomic robots connected by a deformable tube to efficiently manipulate objects of irregular shapes toward target locations. To autonomously perform this task, we develop a local integrated planning and control strategy that solves the problem in two steps (viz. enveloping and transport) based on the model predictive control (MPC) framework. The deformable underactuated system is simplified by a linear kinematic model. The enveloping problem is formulated as the minimization of multiple criteria that represent the enclosing error of the object by the variable morphology system. The transport problem is tackled by formulating the non-prehensile dragging action as an inequality constraint specified by the body frame of the deformable system. Reactive obstacle avoidance is ensured by a maximum margin-based term that utilizes the system's geometry and the feedback proximity to the environment. To validate the performance of the proposed methodology, we report a detailed experimental study with vision-guided robotic prototypes conducting multiple autonomous object transport tasks.