A word for a form of government that governs itself

The word I think you're looking for may be utopia:

Utopia |yo͞oˈtōpēə|(also utopia )
noun an imagined place or state of things in which everything is perfect. The word was first used in the book Utopia (1516) by Sir Thomas More. The opposite of dystopia. ORIGIN based on Greek ou ‘not’ + topos ‘place.’

Note that such a place, as the Greek derivation shows, does not exist.

Of course, you might mean pantisocracy:

Pantisocracy |ˌpantiˈsäkrəsē|
noun
a form of utopian social organization in which all are equal in social position and responsibility.

But that also points to utopia.

This is a matter of great debate, actually.

Anarchists hold that they represent the ideal you are speaking of. Lots of people oppose them, however, saying that anarchists represent chaos and a breakdown of order. There has never been an agreement on one side or the other about who is right and who is wrong.

"Arch-" is something above, an authoritative body of imposition.

"An-arch" is the absence of an authority enforcing laws; the word itself does not imply a lack of order, so much as a lack of authority. It has been interpreted by some, however, to imply a full lack of order, or complete chaos.

"-cracy" is a pluralistic form of "archy", so "democracy", "plutocracy", etc, all indicate forms of pluralistic authority.

Anarchists assert that they are pursuing a practical utopia; people who support authority dispute that.