Timely and personalized treatment decisions are essential across a wide range of healthcare settings where patient responses vary significantly and evolve over time. Clinical data used to support these decisions are often irregularly sampled, sparse, and noisy. Existing decision support systems commonly rely on discretization and imputation, which can distort critical temporal dynamics and degrade decision quality. Moreover, they often overlook the clinical significance of irregular recording frequencies, filtering out patterns in how and when data is collected. Reinforcement Learning (RL) is a natural fit for clinical decision-making, enabling sequential, long-term optimization in dynamic, uncertain environments. However, most existing treatment recommendation systems are model-free and trained solely on offline data, making them sample-inefficient, sensitive to data quality, and poorly generalizable across tasks or cohorts. To address these limitations, we propose MedDreamer, a two-phase model-based RL framework for personalized treatment recommendation. MedDreamer uses a world model with an Adaptive Feature Integration (AFI) module to effectively model irregular, sparse clinical data. Through latent imagination, it simulates plausible patient trajectories to enhance learning, refining its policy using a mix of real and imagined experiences. This enables learning policies that go beyond suboptimal historical decisions while remaining grounded in clinical data. To our knowledge, this is the first application of latent imagination to irregular healthcare data. Evaluations on sepsis and mechanical ventilation (MV) treatment using two large-scale EHR datasets show that MedDreamer outperforms both model-free and model-based baselines in clinical outcomes and off-policy metrics.