When will the son of a woman be old or mature enough for the woman to be able to travel with him?
Normally the son or mahram has to be an adult for him to serve as mahram for a Muslim women on a journey. However Imam Al-Haskafi mentioned someone close to being an adult can also serve as a mahram and Ibn Abidin concurred with this opinion:
مَعَ (زَوْجٍ أَوْ مَحْرَمٍ) وَلَوْ عَبْدًا أَوْ ذِمِّيًّا أَوْ بِرَضَاعٍ (بَالِغٍ) قَيَّدَ لَهُمَا كَمَا فِي النَّهْرِ بَحْثً
(عَاقِلٍ وَالْمُرَاهِقُ كَبَالِغٍ)
“[She must travel] With her husband or mahram (unmarriageable relative) even if he is a bondservant, non-Muslim or related by suckling. He, the husband or Mahram, must be an adult as mentioned in ‘Al-Nahr ‘(book of Hanafi Fiqh). The murahiq (adolescent) is similar to the adult. Him being sane is also a condition.”
(Al-Durr al-Mukhtar, Chapter of Hajj)
As for adulthood according to the Hanafi School this occurs for a male between the ages of 12 and 15 (lunar years). It is established by the male have nocturnal emission (or emission during the daytime) between these years. If the male does not experience this and reaches the age of 15 (lunar years) then he is automatically considered an adult.
As for the definition of murahiq, this is provided by Imam Ibn al-Humam in Fath al-Qadir. Where he mentioned it is someone who is 12 or 13 years old. So a murahiq is someone who is in the age bracket of becoming an adult but has not yet seen the sign of adulthood (nocturnal emission):
بِخِلَافِ الْمُرَاهِقِ وَحدَهُ ثَلَاثَةَ عَشَرَ أَوْ اثْنَتَا عَشَرَ سَنَةً
[And a woman is not permitted to travel with] a non murahiq (adolescent) male. As for the murahiq (adolescent) it is permitted. The murahiq is someone at the age of 12 or 13.”
(Fath al Qadir, Chapter of Maintenance)