It varies from culture to culture. In western culture, as soon as u turn adult & become self independent it would b alright if u move on.
In eastern culture, theres the concept of combined families where a son would live with his wife, children & parents altogether. In such scenarios, If someone leaves his/her parents after becoming self independent, society might title him as a selfish child. Rationally both cultural traits possess certain strengths & flaws. Statistically, we find relatively higher emotional bonding in combined families where as nuclear families are considered more mentally strong & possess the ability to produce more responsible persons for the society.
Theres no specific time for doing it. I would personally suggest to go for a win-win situation. Let ur parents decide wat do they really want & then decide what do u want,try to make it a synergistic effect!