While collective and individual self-defense would still be allowed, since there's no gov't obviously, but you'd have a hard time convincing me its more efficient to constantly be defending yourself from other people, not to mention other states, rather than have a police or military.
Actually you do need a state to decide who has violated non-aggression principles, or has committed fraud, contract violation, etc. If you have a system which punishes people for these actions, then you have laws against them, then you have a government, that is the exact definition of one. The definition of sovereignty is a monopoly on violence in a particular area and via this monopoly of violence the gov't can make and enforce laws, this is exactly what you are talking about here.
You are arguing that a gov't doesn't need to exist to monitor people because people can just form a gov't to monitor themselves.