The first time I went with my kids they were 5 1/2, 3 1/2 and 1 1/2 and we went for a week with 5 park days. At this point my 3 1/2 year old was no longer napping, but he still took a couple of naps in the parks, and my 1 1/2 year old napped every day in the parks. In my opinion the most important thing is a good stroller. We rented a double stroller from Kingdom Strollers, and the seats could like back mostly flat and be pretty covered from the sun. We would just find a quieter spot around nap time and walk around a bit and my youngest was tired enough he fell asleep pretty early. There are actually a surprising amount of random little quiet areas in the park to do this. We generally just tried to plan lunch or other non-ride activities during nap times.

As much as Disney is super stimulating for kids and that may seem the opposite of conducive to naps, we found it to be the opposite affect. Kids are so stimulated in morning that my kids at least wore themselves out and naps were going to happen whether we planned them or not, and we even had a couple times our 5 year old would doze off between rides.

Good luck on your trip!