Should a 3.5 year old have a nap? ?

My daughter stopped napping about 4 months ago and will only nap if it's mid afternoon car ride and then I have to carry her in. If she does nap it's for 2 - 3 hours though as she's always been a pretty good napper. I don't understand though how she can go for 12 - 13 hours straight without dropping. I'm a stay at home Mom and I could crash at night right after she does. I have tried, when naps started tapering off, to get her to nap and she just won't. She'll have a complete meltdown and won't just lay down to rest unless we're watching a movie, but she's never fallen asleep to a movie.