Hajj of Boys (Ahadith 1575 - 1578)

Bismillah.
Volume 3, Book 29, Number 80:
Narrated Ibn 'Abbas (radiallaahu `anhu):
The Prophet (sallallaahu `alayhi wasallam) sent me (to Mina) with the luggage from Jam' (i.e. Al-Muzdalifa) at night.

Volume 3, Book 29, Number 81:
Narrated 'Abdullah bin 'Abbas (radiallaahu `anhu):
I came riding on my she-ass and had (just) then attained the age of puberty. Allah's Apostle (sallallaahu `alayhi wasallam) was praying at Mina. I passed in front of a part of the first row and then dismounted from it, and the animal started grazing. I aligned with the people behind Allah's Apostle (sallallaahu `alayhi wasallam) (The sub-narrator added that happened in Mina during the Prophet's Hajjat-ul-wada.)

Volume 3, Book 29, Number 82:
Narrated As-Sa'ib bin Yazid (radiallaahu `anhu):
(While in the company of my parents) I was made to perform Hajj with Allah's Apostle (sallallaahu `alayhi wasallam) and I was a seven-year-old boy then.

Volume 3, Book 29, Number 83:
Narrated Al-Ju'aid bin 'AbdurRahman:
I heard 'Umar bin 'Abdul Aziz telling about As-Sa'ib bin Yazid that he had performed Hajj (while carried) with the belongings of the Prophet (sallallaahu `alayhi wasallam).
Children who have not yet reached the age of puberty will be rewarded for the good deeds they do. Ibn ‘Abbaas (may Allaah be pleased with them both), said: “A woman lifted up a child and said, ‘O Messenger of Allaah, will his Hajj (pilgrimage) be counted?’ He said, ‘Yes, and you will be rewarded.’” [Muslim]
The author of Mawaahib al-Jaleel said, concerning children entering ihraam (sacred state) for Hajj and ‘Umrah:
“The scholars do not differ concerning the fact that children will be rewarded for whatever acts of obedience (to Allaah) they do, and will be let off for any bad deeds that they do, and any bad deeds they do deliberately will be counted as mistakes. It says in Mukhtasar al-Waadihah: ‘Hajj is not an obligation for boys and girls until boys reach puberty and girls begin menstruating, but there is nothing wrong with taking them for Hajj. It is recommended (mustahabb), and the Messenger of Allaah (peace and blessings of Allaah be upon him) did so.’”
Then he reported that Talhah ibn Musarrif said: “It was one of the customs of the Muslims to take their children for Hajj and expose them to the mercy of Allaah.”
Ibn ‘Abd al-Barr said in al-Tamheed that it is encouraged to take children for Hajj, and that the majority of scholars say this. He also said: “It is nothing strange that a child should earn reward and status in the Hereafter for his salaah (prayers), zakaah (paying poor-due), Hajj and other good deeds if he does them as they should be done, (because this is) grace and mercy from Allaah, just as Allaah shows mercy to the dead by rewarding them for acts of charity done on their behalf by the living. Do you not see that they (the scholars) are agreed that a child should be commanded to pray when he reaches the age of understanding and that the Prophet (peace and blessings of Allaah be upon him) led Anas and the orphan in prayer? Most of the salaf (pious predecessors) said that zakaah has to be paid on the property of orphans, and it is impossible that they would not be rewarded for that. Their guardians and the one who does this on their behalf will also certainly be rewarded, as will the one who takes them for Hajj, as a blessing and mercy from Allaah. It was reported that ‘Umar said: ‘Children’s good deeds will be recorded and their bad deeds will not be recorded.’ I do not know of anyone whose opinion is worth following who said anything to the contrary.”
More on it here.