When I was in my panic mode about DD's preschool and what an awful choice we made I knew I couldn't let her finish up the year, but with DD we saw major differences in her. Even though I wasn't comfortable leaving her in the school for the rest of the year I would have been fine with another month while I searched for another school. We just lucked out that the school remembered her and her abilities and took her over people on the waiting list. (She had done their summer camp for 3 weeks.) So we were able to move her within a week.

If you're moving and starting another school in a month I wouldn't stress over his time at the school.