And there two issues. One, the Quran does not set a minimum age of marriage. In fact, it suggests that men can divorce female before they menstruate - that is before puberty!

In this verse, the Quran sets the conditions to when to have intercourse with women you marry after she is divorced- to ensure a child you get from them is yours. 

"And those who no longer expect menstruation among your women - if you doubt, then their period is three months, and [also for] *those who have not menstruated* ...."

Quran 65:4

- Feel free to check all the tafsers (explanations) that refer to underage girls!And then comes many *authentic* Hadith about the age of Aisha at marriage.

Narrated Hisham's father: Khadija died three years before the Prophet departed to Medina. He stayed there for two years or so and then he married 'Aisha when she was a girl of six years of age, and he consumed that marriage when she was nine years old. (Bukhari 3896)Narrated 'Aisha: that the Prophet married her when she was six years old and he consummated his marriage when she was nine years old, and then she remained with him for nine years (i.e., till his death). Bukhari (5134)Narrated 'Aisha: I used to play with the dolls in the presence of the Prophet, and my girl friends also used to play with me. When Allah's Apostle used to enter (my dwelling place) they used to hide themselves, but the Prophet would call them to join and play with me. (The playing with the dolls and similar images is forbidden, but it was allowed for 'Aisha at that time, as she was a little girl, not yet reached the age of puberty.) Bukhari 6130I hear you say, this is Bukhari, maybe he is a liar!! Here is Sahih Muslim.

'A'isha (Allah be pleased with her) reported: Allah's Apostle (may peace be upon him) married me when I was six years old, and I was admitted to his house when I was nine years old.'

Muslim (1422b)