I didn't read the article you linked to, but I have read countless texts claiming that it's Islamically forbidden to have a woman as a head of state, or in any leading position for that matter.
Usually, they ignore the story of the queen of Sheba though and refer to 4:34 and to the much-quoted hadith that a nation being led by a woman will never prosper. And then they usually get into all this crap about women's supposed intellectual deficiencies, menstruation, duty to care for kids, lack of logic etc. pp.
What the author of your above quote writes about the queen of Sheba is absolute rubbish. There is nothing in that story in the Qur'an to conclude that Solomon attacked her because of her gender, or that God disapproves of a woman as a leader of a nation. The queen of Sheba is praised for her intelligence, intuition etc.; her people and her advisors trust her ability to make decisions regarding the benefit of her people, she is depicted as a very strong and positive personality.
So that story in fact proves that if we look at the Qur'an for guidance, there is nothing to ban women from leading positions.
Btw., I highly recommend Fatima Mernissi's "The Veil and the Male Elite". It addresses this and other, related, issues, is well-researched and a really good read if you're interested in women's rights in Islam.
And Solomon's soldiers were gathered, comprising of humans and Jinn and birds, for they were to be spread out.
Until they came to a valley of ants, a female ant said: "O ants, enter your homes else you will be crushed by Solomon and his soldiers while they do not notice."
He then smiled, amused by what she said. And he said: "My Lord, help me to be thankful for the blessings You have bestowed upon me and upon my parents, and that I may do good work that pleases You, and admit me by Your Mercy with Your righteous servants."
And he inspected the birds, then said: "Why do I not see the hoopoe, or is he among those absent?"
"I will punish him severely, or I will kill him, else he should have a clear excuse."
But the hoopoe did not stay away long, then he said: "I have seen what you do not know, and I have come to you from Sheba with news which is certain."
"I found them ruled by a woman, and she was given all possession, and she had a great throne."
"And I found her and her people prostrating to the sun instead of God! And the devil had made their work appear good to them, so he kept them away from the path, for they are not being guided."
"Will they not prostrate to God who brings out what is hidden in the heavens and the Earth, and He knows what you hide and what you declare?"
"God, there is no god but He, the Lord of the great throne."
He said: "We will see if you are being truthful or are one of those who lie."
"Take this letter of mine and deliver it to them, then withdraw from them and observe what they respond with."
She said: "O commanders, a noble letter has been delivered to me."
"It is from Solomon, and it reads: "In the name of God, the Almighty, the Merciful""
""Do not be arrogant toward me and come to me as submitters""
She said: "O commanders, advise me in this matter of mine, for I will not take a decision until you give testimony."
They said: "We are people of strength and mighty in power. But the decision is yours, so see what you will command."
She said: "When the kings enter a town they destroy it and make its most noble people humiliated. It is such that they do."
"And I will send to them a gift, then I will see with what the messengers will return."
So when they came to Solomon he said: "Are you providing me with wealth? What God has provided for me is far better than what He has given you. Now you are happy with your gift!"
"Return to them. For we shall come to them with soldiers the like of which they have never seen, and we will drive them out humiliated, while they are feeble."
He said: "O commanders, which of you can bring me her throne before they come to me in submission?"
A powerful being from among the Jinn said: "I will bring it to you before you rise from your station. For I am strong and trustworthy."
And one who had knowledge from the Scripture said: "I will bring it to you before you blink." So when he saw it resting before him, he said: "This is from the grace of my Lord, so that He tests me whether I am thankful or whether I reject. As for he who is thankful, he is thankful for himself, and as for he who rejects, then my Lord is Rich, Bountiful."
He said: "Disguise her throne so we may see if she will be guided or if she will be of those who are not guided."
So when she came, it was said: "Is your throne like this?" She said: "It appears to be similar." And we were given knowledge before her, and we had submitted.
And she was prevented by that which she served besides God. She was of the people who were rejecters.
It was said to her: "Enter the palace." So when she saw it she thought there was a pool, and she uncovered her legs. He said: "It is a palace paved with crystal." She said: "My Lord, I have wronged myself; and I submit with Solomon to God, the Lord of the worlds."