According to Islam, divorce can only be carried out by the husband, therefore, the wife cannot divorce herself and not paying the Nafaqah doesn’t give her the permission to be able to do so. Subsequently, there is no waiting period of iddah for her. However, the wife can refer to the Islamic authority (Hakim Shar’) and express her problem of not being given Nafaqah, and make an appeal not only for receiving Nafaqah, but also for divorce by the authority, who in turn can force the husband to pay it and if necessary, he (the authority) can legally divorce her in his absence.
In any case, if the husband doesn’t pay her the Nafaqah without any legally acceptable excuse, the Islamic authority can divorce her from her husband and she will have to observe the waiting period after the divorce has been executed.
Fortunately, given the means of communication in today’s world, Muslim women can engage in solving their problems of this genre.
Response of the office of Ayatullah Makarim Shirazi (may Allah prolong his life):
In the case of the husband not paying the Nafaqah without any legally acceptable excuse, the Islamic authority can legally divorce her from him. The waiting period will begin after the divorce formula has been carried out.
Response of the office of Ayatullah Fazel Lankarani (RAH):
No, she must refer to the courts. The waiting period begins when the divorce formula has been carried out.
Response of the office of Ayatullah Bahjat (RAH):
No, she cannot and she must ask the husband to divorce her so that if he wants, he does so.
 Tahrir al-Wasilah, kitab al-talaq (book of divorce), pg. 763, issues 1,2 and 3.
 What is meant by the Islamic authority, is the qualified jurist (mujtahid).