How do you get along with your parents? Are they hinting for you to move out, do they support you at home or otherwise not making you pay rent? If they're happy for you to live with them for free then stay at home. You say you want to save up some money to move out - the moving out comes after some money is saved, not before
Keep your relationship with your girlfriend the way it is, get some money together and enjoy living at home, I say. If you don't need to move out then don't!