Have the Allies decided who will be in charge of preserving order and providing government services between the time Muammar Qaddafi is overthrown and a new government can be established?
Democracies don't miraculously appear after the overthrow of tyrants. Working out differences about what type of government is desired takes time. Someone has to run the interim government until differences can be resolved like the U.S attempted to do in Iraq.
Iraq isn't the only country that has had trouble developing a democratic government to replace a tyrant. Examples from European history demonstrate that the difficulties of establishing democratic government to replace tyrants.
The overthrow of the French monarchy in the late 18th Century was followed by various governments until a new strongman named Napoleon was able to establish a stable government. He then decided to expand the size of his empire to include most of Europe into Russia.
The fall of the Russian monarchy late during World War I also eventually produced a tyrant with a desire for empire. An initial attempt at democracy failed and the country descended into chaos with the communist party led by Lenin eventually conquering the country. His successor Joseph Stalin used the situation after World War II to expand the country's boundaries into Eastern Europe.
The Allied attack on the Libyan military means it will not be available to reestablish order even if people would accept its leaders after their efforts to keep Qaddafi in office. The problems other governments in the area are having mean they cannot assist with reestablishing order in Libya. One or more of the Allies will have send in a caretaker force to run things.
Qaddafi has many loyal supporters, particularly among those who have benefited from his rule, who might use guerrilla tactics against the interim government as happened in Iraq. Al Qaeda will certainly be interested in attempting to take advantage of the situation and use terrorism to force the interim government out as happened in Iraq.
The lawlessness in Somalia demonstrates what can happen without a government capable of establishing order.