It is stipulated that the mahram who is going to travel with a woman should be an adult

Praise be to Allah.

What is required of the Muslim is to obey the commands of Allah and not pay any attention to what people say. Allah, may He be exalted, says (interpretation of the meaning):

“It is not for a believer, man or woman, when Allah and His Messenger have decreed a matter that they should have any option in their decision. And whoever disobeys Allah and His Messenger, he has indeed strayed in a plain error”

[al-Ahzaab 33:36]. 

Your resolve to obey Allah and follow His commands is to be appreciated, and we ask Allah to increase you in guidance. 

Secondly: 

It is stipulated that the mahram who is going to travel with a woman should be an adult, because the purpose of having a mahram with her is to look after the woman and protect her, and this cannot be done by the one who is not yet adult. 

Shaykh Ibn Baaz (may Allah have mercy on him) was asked: What is the minimum age for a youth to be a mahram for a woman if she wants to travel? 

He replied: 

The minimum age for a man to be a mahram for a woman is puberty, which is when a boy reaches the age of fifteen years, or maniy is emitted with desire, or coarse hair grows around the private part. 

If one of these three signs is present, the male is now regarded as accountable as it is permissible for him to be a mahram for the woman.

End quote from Majmoo‘ al-Fataawa, 16/382 

And Allah knows best.