Full-duplex spoken dialogue models, which process audio input and output simultaneously, have been actively studied for their ability to naturally model turn-taking and non-verbal phenomena in addition to generating responses. Although these models enable natural conversational flow, they lack mechanisms for language understanding and dialogue management, making them difficult to apply to task-oriented dialogue systems. We propose a method for incorporating dialogue state tracking in task-oriented dialogue into Moshi, aiming to achieve a multi-channel, full-duplex task-oriented spoken dialogue model. We evaluated the proposed method on JMultiWOZ, a benchmark corpus for Japanese task-oriented dialogue, focusing on dialogue state tracking and response generation.