Large Language Models (LLMs) have revolutionized the field of artificial intelligence (AI) through their advanced reasoning capabilities, but their extensive parameter sets introduce significant inference latency, posing a challenge to ensure the timeliness of inference results. While Small Language Models (SLMs) offer faster inference speeds with fewer parameters, they often compromise accuracy on complex tasks. This study proposes a novel remote inference system comprising a user, a sensor, and an edge server that integrates both model types alongside a decision maker. The system dynamically determines the resolution of images transmitted by the sensor and routes inference tasks to either an SLM or LLM to optimize performance. The key objective is to minimize the Task-oriented Age of Information (TAoI) by jointly considering the accuracy and timeliness of the inference task. Due to the non-uniform transmission time and inference time, we formulate this problem as a Semi-Markov Decision Process (SMDP). By converting the SMDP to an equivalent Markov decision process, we prove that the optimal control policy follows a threshold-based structure. We further develop a relative policy iteration algorithm leveraging this threshold property. Simulation results demonstrate that our proposed optimal policy significantly outperforms baseline approaches in managing the accuracy-timeliness trade-off.