So here are my two questions:
first, should I be concerned that I have only found one egg so far or do I just need to be patient?
second, is there any reason the queen would not be ok after her excursion outside the hive?
Thanks for any information or advice you might have.
1) Eggs can be hard to see on newly drawn foundation. Are you certain the one you did see was an egg? One just seems odd, and the fact that it was on the side of the cell and not the bottom usually indicates a laying worker, but I wouldn't jump to that conclusion with just one egg. I would give her some more time and see if you see more eggs or larvae. You could have been shipped a virgin queen and she may have taken a few days to mate also.
2) She should be fine. I've had them fly away and have them come back. I have also found one on the ground the day after an inspection and still be fine when put back in the hive.