If a woman got divorced from her husband cause she hates him and doesn't want him and he didn't have sex with her must she wait for 3 month to marry again?

Praise be to Allah, the Lord of the World; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

In spite of the fact that divorce and Khula' (divorce in return for a monetary compensation to be paid by the wife to the husband) are lawful in Sharia, one should not undertake either unless it becomes impossible for the couples to live with cordiality and kindness.
However, if divorce or Khula' occurs, a divorced or repudiated woman should enter upon 'Iddah (three periods of menstruation for one who is not pregnant, three months for a woman who has no menstruation, and if one is pregnant till she gives birth to child).
As a rule, entering upon 'Iddah is mandatory even though it becomes clear that there is no pregnancy since this is not the only wisdom of 'Iddah.
'Iddah is enjoined to prepare the couple to resume their normal life if possible. Also, it is imposed to show that marriage, in Islam, ranks high. Another lesson of imposing 'Iddah is to teach people that dissolving a contract of marriage is as important as contracting marriage, since both necessitate witnesses and proclamation. Otherwise, marriage will be just a form of play.
Allah Says (interpretation of meaning): {…And those are the set limits of Allâh. And whosoever transgresses the set limits of Allâh, then indeed he has wronged himself. …}[65:1].
Allah knows best.