I think its up to you, but my girls were alot older when I first left their nappy off over night.
Some kids do just do it. I know 2 little girls who were trained over night at 2. My DD1 was 3 & 4 months when she first had no nappy & DD2 was 4.5. Only a few months ago. DD1 still wet the bed til she was 6, DD2 still does, but less than DD1 did at the same age.
I had DS nappy free over night a few months ago, but they've had to go back on as he's been wetting more in the cooler weather. He still wakes up dry most nights though.