Since you ask about "your" ideal anarchist society, I'll answer this question personally, with the understanding that no one assumes this to be a standard or majority anarchist answer.
Hopefully all anarchists would agree that there would be no police or jails (although no doubt there are some who do not). To get more specific, I would prefer to leave the ruins of a couple jails so anyone can wander through them, peer into the few remaining cells, and shiver at the brutality of a society that forced people to live inside them.
I agree with dot that the term "community" needs to be problematized. I do not think that any of us currently have communities, and contemporary forms of responding to harm based on "community accountability" strike me as, at best, an optimistic euphemism, and at worst, a total sham and power play.
In the future community I imagine, in which people are socially and materially interdependent but also as mobile as they choose, the community would sure as shortcake defend itself. We would have the recent, shared memory of banding together to overthrow the government and defeat the very worst psychopaths imaginable (cops, politicians, landlords, etc.) We would still have our guns and our determination to never be ruled again, and I seriously doubt we would be vulnerable, even with the absence of any specialized protection service.
Forms of harm that arise within this community would be dealt with chaotically, by different people in different ways, some offering support, some trying to mediate, some criticizing and pressuring those they see as wrong to change their ways, some breaking connections, and some taking revenge. This is what anthropologists refer to as "diffuse sanctions." The question as to whether this "works" cannot be taken seriously, as it is the most common method in human history. The question for anarchists would be, is this what we want?
As for the truly gruesome acts that are today punished as major crimes, I think it should be said that it is a much healthier dynamic if someone reacts from the gut and kills the other person as an act of vengeance, triggering more conflict in the community as to whether or not that was really okay, than to force everyone to agree on one sanction for the offender, and hide behind a curtain of social legitimacy, excusing in advance as "justice" whatever brutal punishment is agreed upon. The practice of justice is much more oppressive than the outrages committed by people taking things into their own hands.
And no, societies lacking a centralized mechanism of deciding on and dispensing justice did not fall apart in internecine warfare and feuding, so please avoid that Hobbesian fantasy.