First of all, I understand your emotions, we all want to protect and make the world better for our children. However you can not always make things better for him, he has to figure out on his own (and yes even at age 6) how to handle things, he won't always be in classes with his best friends, he will have to learn to make new best friends. I would mention the girl to the teacher, but I would not ask for him to be moved. If his emotional behaviors continue, I know you don't want to hear this, none of us do, you might consider contacting the schools counselor/social worker. There might be some school anxieties that need to be dealt with. But as for now, tell the teacher about the girl, see if you can set up and award system for having good days (not food) and reinforce that school is fun, and ask him about his day (one easy way to get kids to talk about school is to ask what they didn't like first and then say "well, that was bad, what happened that was good?" It is okay to be nervous and upset when you are young, some kids take longer to adjust, but don't fix things for him, let him work it out. If it doesn't get better, then take those extra steps by talking to the school. Relax, he will get through this, your job as the mom is to be there to comfort him when he comes home, let him know that everything is good, but let him find his own way to handle this.
cheer up, it will only get better!!!