Identifying the dynamic properties of manipulated objects is essential for safe and accurate robot control. Most methods rely on low noise force torque sensors, long exciting signals, and solving nonlinear optimization problems, making the estimation process slow. In this work, we propose a fast, online learning based inertial parameter estimation framework that enhances model based control. We aim to quickly and accurately estimate the parameters of an unknown object using only the robot's proprioception through end to end learning, which is applicable for real-time system. To effectively capture features in robot proprioception affected by object dynamics and address the challenge of obtaining ground truth inertial parameters in the real world, we developed a high fidelity simulation that uses more accurate robot dynamics through real-to-sim adaptation. Since our adaptation focuses solely on the robot, task-relevant data (e.g., holding an object) is not required from the real world, simplifying the data collection process. Moreover, we address both parametric and non-parametric modeling errors independently using Robot System Identification and Gaussian Processes. We validate our estimator to assess how quickly and accurately it can estimate physically feasible parameters of an manipulated object given a specific trajectory obtained from a wheeled humanoid robot. Our estimator achieves faster estimation speeds (around 0.1 seconds) while maintaining accuracy comparable to other methods. Additionally, our estimator further highlight its benefits in improving the performance of model based control by compensating object's dynamics and reinitializing new equilibrium point of wheeled humanoid