Here is a timeline:
Got my hive May 15th. The bee man had set it up new about 6 weeks earlier. We robbed it late July (a little too late I was told as the bees were a bit crowded.) 3 1/2 weeks later the bees swarmed. To make sure the bees would adapt to their new home, we took one brood frame out of the original hive and put it in the new hive. The super was not full, but it was very close (I am AMAZED at how fast bees can replenish the honey!) and so we robbed that at the same time.
In the original hive there were about 6 or 7 queen cells, two of which had already hatched. I can't remember if we put one of the frames with queen cells in the new hive. I kinda doubt it, but am not 100% sure.