Hello Michelle!
We moved when my son was 3 weeks old. We waited until after he was born, and I am glad we did. Though I had to have someone watch my baby for most of the day, it was a lot easier than I thought. Since we knew we were moving afterwards, we didn't set up his crib or put any of his furniture together, just his bassinet, pack and play, and swing. I put all of his clothes in one box and rotated through as needed. My husband and I worked hard to get all we could get done before he came. And like the other poster said, it will be very difficult to find someone to take you in as a patient last minute. I would secure a place ahead of time, but don't move until afterwards. Even then, give it a few weeks so you can get your strength up.