When should I move out?

i think you should move out whenever you want to and whenever you feel youre ready to

From a financial perspective, the longer you're there the more you can save, assuming your parents aren't charging you rent. However, do you live in a college town? Remember that end of summer is when the most college kids are moving out of parent's houses, so rents will likely be higher overall that it would at the beginning of summer when many kids move out and return home for the summer, or in say October - December when move ins aren't common and rents might be more favorable.

I recommend talking it over with your parents, and not random strangers on the internet. They know you best, and own the house. They also know the rest of the picture as to how capable you are of paying your own way - we have no idea.