Not sure about Qur’an and Sunnah but according to Islamqa the father has right to get her minor girl married off . Now, Islamqa is not the final authority on Islam but it is the majority scholar view.

https://islamqa.info/en/answers/27305/marrying-a-thirteen-year-old-girl

The validity of marriage to a minor girl is proven by the words of Allaah (interpretation of the meaning):

“And those of your women as have passed the age of monthly courses, for them the ‘Iddah (prescribed period), if you have doubt (about their periods), is three months; and for those who have no courses [(i.e. they are still immature) their ‘Iddah (prescribed period) is three months likewise, except in case of death]”

[al-Talaaq 65:4]

So the ‘iddah for those who do not menstruate because they are too young is three months, and ‘iddah has to do with divorce after getting married, which indicates that the girls in question has been married and divorced.

If she has not reached the age of puberty, then her father has the sole right to arrange her marriage and does not have to ask her permission.

4:19 prohibits it

@Rafo http://www.answeringislamicskeptics.com/age-of-marriage-in-islam.html

The tafsir of 65:4 from Maududi :

Here, one should bear in mind the fact that according to the explanations given in the Qur’an the question of the waiting period arises in respect of the women with whom marriage may have been consummated, for there is no waiting-period in case divorce is pronounced before the consummation of marriage. (Al-Ahzab: 49). Therefore, making mention of the waiting-period for the girls who have not yet menstruated, clearly proves that it is not only permissible to give away the girl in marriage at this age but it is also permissible for the husband to consummate marriage with her. Now, obviously no Muslim has the right to forbid a thing which the Qur’an has held as permissible.

Tafsir : Jalal – Al-Jalalayn

And [as for] those of your women who (read allā’ī or allā’i in both instances) no longer expect to menstruate, if you have any doubts, about their waiting period, their prescribed [waiting] period shall be three months, and [also for] those who have not yet menstruated, because of their young age, their period shall [also] be three months — both cases apply to other than those whose spouses have died; for these [latter] their period is prescribed in the verse: they shall wait by themselves for four months and ten [days] [Q. 2:234]. And those who are pregnant, their term, the conclusion of their prescribed [waiting] period if divorced or if their spouses be dead, shall be when they deliver. And whoever fears God, He will make matters ease for him, in this world and in the Hereafter.

Anyway- some people don’t menstruate until 16. So the verse could be taken to mean that they have achieved mental understanding but not physical maturity. Mental understanding is a requirement as per other places. Please refer to the link I sent

This tafasir also says “too young” .

Abbas – Tanwîr al-Miqbâs min Tafsîr Ibn ‘Abbâs

(And for such of your women as despair of menstruation) because of old age, (if ye doubt) about their waiting period, (their period (of waiting) shall be three months) upon which another man asked: “O Messenger of Allah! What about the waiting period of those who do not have menstruation because they are too young?” (along with those who have it not) because of young age, their waiting period is three months. Another man asked: “what is the waiting period for those women who are pregnant?” (And for those with child) i.e. those who are pregnant, (their period) their waiting period (shall be till they bring forth their burden) their child. (And whosoever keepeth his duty to Allah) and whoever fears Allah regarding what he commands him, (He maketh his course easy for him) He makes his matter easy; and it is also said this means: He will help him to worship Him well.