Whenever you are ready to, from the age I started working full time (17) I would pay my way monthly in my parents house just so I understood the value of money properly, so i would know it will be like when that time comes to move out.
That being said I moved out at the age of 20 with my girlfriend, rented for 5 years and now have a mortgage on that very same home as of June last year, now I have son who's 3 weeks old. It's all about when you are ready and can have stability, don't rush to move out if a couple months down the line you are going to be moving back.