I did without a car during training and it was just fine. I was put on reserve right as I finished IOE. But I called the Chief Pilot and asked if I could have a little more time. He gave me one personal day, which at least gave me time at least to get some things together for the crashpad. But if you tell him you are flat out moving, he may give you a few more. If not, you'll just have to wait until you have a group of days off. What part of NY are you going to move to?