“Furthermore, I highly doubt that if a student would disappear, Dumbledore’s first reaction would be to suspect a teacher of abducting the student, much less Moody whom he specifically brought in to increase security and trusts implicitly.”
Read my post. I never said he would suspect Moody. I said he would question him. Meaning, gather the teachers and tell them the news, and ask if they saw/heard anything suspicious etc. He would be sure to question Moody particularly, who was supposedly once one of the best aurors and is more likely to have seen something suspicious going on in the castle (being that he can see through walls and all)