As stated before, Quinn being in the position he was in, was free to leave as he wished. Even if he had classes to teach, such as the homeroom class and the beast weapons class, he just needed to inform them beforehand and that's exactly what he did.
To his surprise, the person who would be taking his homeroom class was Hayley. Honestly, Quinn was quite happy with the choice, considering how well the class had reacted to her the last time she had taught. On top of this, he remembered the times when he was at school and would often have to come to the medical room.