Space free-flyers like the Astrobee robots currently operating aboard the International Space Station must operate with inherent system uncertainties. Parametric uncertainties like mass and moment of inertia are especially important to quantify in these safety-critical space systems and can change in scenarios such as on-orbit cargo movement, where unknown grappled payloads significantly change the system dynamics. Cautiously learning these uncertainties en route can potentially avoid time- and fuel-consuming pure system identification maneuvers. Recognizing this, this work proposes RATTLE, an online information-aware motion planning algorithm that explicitly weights parametric model-learning coupled with real-time replanning capability that can take advantage of improved system models. The method consists of a two-tiered (global and local) planner, a low-level model predictive controller, and an online parameter estimator that produces estimates of the robot's inertial properties for more informed control and replanning on-the-fly; all levels of the planning and control feature online update-able models. Simulation results of RATTLE for the Astrobee free-flyer grappling an uncertain payload are presented alongside results of a hardware demonstration showcasing the ability to explicitly encourage model parametric learning while achieving otherwise useful motion.