Mobile robots exploring indoor environments increasingly rely on vision-language models to perceive high-level semantic cues in camera images, such as object categories. Such models offer the potential to substantially advance robot behaviour for tasks such as object-goal navigation (ObjectNav), where the robot must locate objects specified in natural language by exploring the environment. Current ObjectNav methods heavily depend on prompt engineering for perception and do not address the semantic uncertainty induced by variations in prompt phrasing. Ignoring semantic uncertainty can lead to suboptimal exploration, which in turn limits performance. Hence, we propose a semantic uncertainty-informed active perception pipeline for ObjectNav in indoor environments. We introduce a novel probabilistic sensor model for quantifying semantic uncertainty in vision-language models and incorporate it into a probabilistic geometric-semantic map to enhance spatial understanding. Based on this map, we develop a frontier exploration planner with an uncertainty-informed multi-armed bandit objective to guide efficient object search. Experimental results demonstrate that our method achieves ObjectNav success rates comparable to those of state-of-the-art approaches, without requiring extensive prompt engineering.