Self-modeling refers to an agent's ability to learn a predictive model of its own behavior. A continuously adapted self-model can serve as an internal simulator, enabling the agent to plan and assess various potential behaviors internally, reducing the need for expensive physical experimentation. Self-models are especially important in legged locomotion, where manual modeling is difficult, reinforcement learning is slow, and physical experimentation is risky. Here, we propose a Quasi-static Self-Modeling framework that focuses on learning a predictive model only of high-level quasi-static dynamics, rather than a continuous model. Experimental results on a 12-degree-of-freedom-legged robot demonstrate improvements over model-free and traditional model-based continuous approaches. Using 80 diverse robot morphologies, we confirm a correlation of R2=0.94 between the improvements rendered by our method and the DoF of the robot, suggesting that as future robots increase in complexity, this approach will become more valuable.