K.,
When my twins, now 9 were about that age, they stopped all together taking naps. They were late sleepers, like 9:30 or so in the morning, so by 12:oopm they weren't ready for a nap. It did take them a few days to adjust not taking a nap, but I had to much to do to lay around until they both fell asleep. Plus this is such a bad habit to start. I started it and it was soo hard to break. I did not do this with our second child.
I used this to my advantage because they were in bed usually asleep by 7:30pm-7:45pm. This was great because my husband and I could have quiet time(romance before 10pm when were both exhausted), watch a movie, or read a book, or just do a load of laundry and not have it pulled off the couch after I just folded it. Or just do nothing at all and get an extra hour or two of sleep.
Good luck, Trish