Leaving so soon after school starts may present a little more of a problem. The teacher will have less time to prepare...but who knows, maybe they already have stuff prepared for that far into the school year.
We have gone several times during the school year and our kids have missed a week each time. My hubby is a farmer and summer is just out of the question for us.
I always go to the principal at the earliest possible date - as soon as we decide to go. Last year I saw him at the before-school-started orientation. He has always verbally approved and asked me to remind him closer to the date of our trip. I usually then approach the teachers. They say the same, let them know closer to time - but this way they already know it is going to happen. (Our last trip was in mid December and everyone knew by September.) Closer to the time of the trip, I present the principal with a written request for my children to have excused absences. He signs it and passes it on to the teachers. At this point, I always have a meeting with each teacher and ask what I can do to make things easier. Without fail, there is something I can do. Furthermore, I always ask for the assignments a full week BEFORE we leave on the trip! They have never minded doing that and that way the kids can actually get ahead and get it done before we go. AND! All except one time, the teacher let them take any tests they were going to miss before we went - that time she didn't have it made out yet. So, there is no huge amount of work after they return. They don't mind doing it so much before they go because the reward is so immediate and clearly attainable: a trip to Disney World!