Is it right to move out with your boyfriend at the age of 18?

That depends on what you mean by "right." If you're 18, you're an adult. If you think you can behave like one and support yourself and believe you're ready to live responsibly and independently, then there's nothing wrong with finding your own place, or sharing one with a roommate. However, many people still look disapprovingly upon people "cohabitating" or living together outside of marriage. Many consider "fornication" -- that is, having sexual relations with someone other than one's spouse -- to be immoral, even sinful. I suspect you don't share those beliefs. If you don't, there's little wrong with what you are proposing.