Hi J.,
Do yourself a BIG favor, and get the book "Healthy Sleep Habits, Happy Child," by Dr. Marc Weissbluth. I'm a mom of 6, and I've used it more times than I can tell you. It's a sanity saver. Believe it or not, the answer to awakening too early in the morning is actually an earlier bedtime. Try making it earlier by 20 minute increments until you achieve a later wake-up time. Also, at 13 months, some kids still need two naps, and some are ready to go to one. I would start with the nighttime, and if he wakes up later, say 6 or 7, try a nap around 10am, and another around 2 or 2:30. Don't start one later than 3, as it will interfere with bedtime. I think you'll find that once he's sleeping better at night, he'll surprise you with also sleeping longer at naptimes.
On another note, I would seriously question a school that does not have a nap time for a 2 or even 3 y.o. My kids all napped until at least three, and most til 4 or 5. Even their kindergarten had naptime.
Anyway, good luck with your sleep scheduling. Definitely get that book -- it's worth way more than the purchase price.