E.T.
We had a similar situation when my girls were 20 months old. We were selling our house and our realtor set up an entire day of showings for other brokers. So we needed to be out of the house from about 9am - 6pm. My girls were (still are) great sleepers but had never really napped anywhere other than our house. We spent the day at a friend's house and I tried to get them to nap there. In truth, it didn't go all that awesome. They did fall asleep eventually, but it was a stressful 1/2 hour for me trying to convince them to sleep. Like you said, though, if they're tired enough, they fall asleep. Mine only napped for about a third of their regular nap time, and then crashed early at bedtime.
Even if your daughter doesn't nap, one day will not set her off and make her all that super cranky. It's the accumulated lack of sleep that really makes kids terrors. Good luck!