A 13 month old is plenty old enough to be taking only one nap per day. That's what she would be used to doing by now if she had already been in child care. At about 10 months the baby room starts transitioning them to the one nap per day so that when they switch rooms on their birthday they are on the same schedule as the other kids in the room. They have a much more scheduled day.
They also start them sleeping on cots so that's not a big deal either when they move up to the toddler room.
I think that she'll get calmed down once she is acclimated to the new situation. She has a lot to deal with right now just getting used to being there. She should start being more in line with their schedule in a month or so at the longest. She really does have to conform. The state licensing worker will make sure the kids are following the required state laws pertaining to how much nap time the kids must have. They don't have to sleep the entire time but they do have to be quiet so the others can sleep.
It may be that she's going to bed way too early too. If you're getting her up at 4am or 5am then perhaps the bedtime is realistic but she may do a lot better if she's not in bed so early. She won't adjust to the new schedule as long as she is sleeping 12-13 hours every night. She won't need a nap at all in a few months and her body really does need to have some down time during the day for at least a couple more years.