As already stated it is well known that Khadijah, the Prophet's first wife arranged her own marriage with the Prophet. It is true that this happened before sayyadna Muhammad received prophethood. But if an arrangement by a woman of her own marriage were so shameful in the eyes of Allah as it is in the eyes of some Muslims, then He would have somehow prevented His Messenger from such a marriage. Moreover, there are some ahadith which show that even after receiving prophethood sayyadna Muhammad did not disapprove of women arranging their own marriage.We quote here one such hadith:
"A woman came to the Messenger of God and offered herself to him (in marriage). When she had stood for a long time (without receiving an answer) a man got up and said: Messenger of God! Marry her to me if you have no need of her. He asked the man if he had anything to give her as dower (marriage gift), and when he replied that he had nothing but the lower garment he was wearing, the Prophet said: Look for something, even though it be an iron ring. Then when the man had searched and found nothing, God's Messenger asked him whether he new anything of the Qur'an. When the man replied that he knew Surah so and so and Surah so and so, God's Messenger said: Go away, I give her to you in marriage. Teach her some of the Qur'an." (Bukhari and Muslim on the authority of Sahl bin Sa'd)
In this hadith a woman is arranging her own marriage but the Prophet does not rebuke her or admonish her in any other way. Thus while it may not be the best thing for a woman to do, she can if she wishes, make a marriage proposal for herself without being blameworthy in the eyes of God.