Is a Child’s Hajj Valid?
Question

Can children be taken along on Hajj? Will Hajj be recorded for them if I perform the rituals on their behalf, or what?.
Praise be to Allah.The sahih Sunnah indicates that a child may do Hajj and be rewarded for it, but that does not count as the “Hajj of Islam” (obligatory Hajj). 
Muslim (2378) narrated that Ibn 'Abbas (may Allah be pleased with him) said: A woman lifted up a child of hers and said: O Messenger of Allah, is there Hajj for this one? He said: “Yes, and you will have the reward.” 
Al-Nawawi said in Sharh Muslim: 
‘This is used as evidence by al-Shafi’i, Malik, Ahmad and the majority of scholars that the Hajj of a child counts and is valid, and he will be rewarded for it, but it does not count as the Hajj of Islam (the obligatory Hajj), rather it is regarded as a voluntary Hajj. This hadith clearly states that.
Al-Qadi said: They are unanimously agreed that it does not count as the obligatory Hajj, which he must do after he reaches puberty, except for a small group who held an odd view and said that it does count. But the scholars did not pay any attention to this view.  
The words of the Prophet (peace and blessings of Allah be upon him) “and you will have the reward” mean that this is because of her carrying him and making him avoid the things that are forbidden to the pilgrim in ihram, and do what the pilgrim does.” 
Al-Khattabi said: 
“It is Hajj for him in the sense of reward , without being counted as Hajj in the sense of obligatory Hajj if he lives until he reaches puberty and becomes a man. This is like prayer; he should be told to pray when he becomes able to pray, although it is not obligatory for him, and the reward will be written for him by the bounty of Allah, and also for the one who tells him to pray and teaches him to do so. If he does Hajj then he must do all the rituals, such as standing in `Arafah and circumambulating around the Ka’bah, being carried if he is unable to walk, and doing sa`i between al-Safa and al-Marwah, and other actions of Hajj.” (`Awn al-Ma’bud) 
Al-Tirmidhi (926) narrated that al-Sa-ib ibn Yazid said: My father took me for Hajj with the Messenger of Allah (peace and blessings of Allah be upon him) during the Farewell Pilgrimage when I was seven years old. (Classed as sahih by al-Albani in Sahih al-Tirmidhi) 
Ibn 'Abbas (may Allah be pleased with him) narrated that the Prophet (peace and blessings of Allah be upon him) said: “Any child who does Hajj then reaches puberty, must do Hajj again.” (Narrated by al-Shafi’i in his Musnad; classed as sahih by al-Albani in Irwa al-Ghalil, 686)
And Allah knows best.