Note that the following answer is purely based on the Islamic point of view in theory. One must be conscious and aware of laws in the land they reside in and not do that which would bring harm to them. The believer must be wise in making decisions.
Praise be to Allaah.
There is nothing wrong with your marrying this girl, even though there is this difference in age between you. What matters is that she should be religiously committed and of good character. These are what matters when it comes to marriage, and are the factors that lead to harmony and happiness in sha Allaah.
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]”
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.
The Prophet (peace and blessings of Allaah be upon him) married ‘Aa’ishah (may Allaah be pleased with her) when she was six years old, and he consummated the marriage with her when she was nine, and at that time he was over fifty.
Al-Bukhaari (3894) and Muslim (1422) narrated that ‘Aa’ishah said: The Prophet (peace and blessings of Allaah be upon him) married me when I was six years old and consummated the marriage with me when I was nine.
A girl who is thirteen years old may have reached the age of puberty, in which case her consent is essential according to the more correct of the two scholarly opinions, because the Prophet (peace and blessings of Allaah be upon him) said: “A previously-married woman should not be married until she has been consulted, and a virgin should not be married until her permission has been sought.” They said: “O Messenger of Allaah, what is her permission?” He said: “If she remains silent.” Narrated by al-Bukhaari, 5136; Muslim, 1419, from the hadeeth of Abu Hurayrah (may Allaah be pleased with him). See also question no. 22760.
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.
Ibn Qudaamah (may Allaah have mercy on him) said: With regard to a virgin who is still a minor, there is no difference of opinion concerning her (i.e., that her father may marry her off even if she objects). Ibn al-Mundhir said: Every scholar from whom we learned was agreed that it is permissible for a man to marry off his virgin daughter who is still a minor, if he marries her to someone who is compatible, and it is permissible for him to marry her off even if she objects and refuses.” Al-Mughni, 9/398
But it was narrated from Imam Ahmad that whoever reaches the age of nine years comes under the same ruling as a girl who has reached puberty, so her permission must be sought. But if the father opts to be on the safe side and ask her permission, that is better. Al-Mughni, 8/398-405.
And Allaah knows best.