can move out legally at age of 21

No legal hurdle is there for you to move out of your house at this age of 21. But socially it may cause you a lot of problems. As a grown up lady you have attained the age of maturity and reason as per Indian laws. Therefore you have every right to do anything as you wish so long as it doesn't go against any law of the land.

am not a lawyer but a parent would request you to think about it more