كتاب الحج
15
The Book of Pilgrimage
(72)
Chapter: Validity of a child's hajj, and the reward of the one who takes him for Hajj
(72)
باب صِحَّةِ حَجِّ الصَّبِيِّ وَأَجْرِ مَنْ حَجَّ بِهِ ‏‏

Karaib reported:

A woman lifted a child and said: Messenger of Allah, would he be credited with Hajj? He said: Yes. and for you there would be a reward.
وَحَدَّثَنِي مُحَمَّدُ بْنُ الْمُثَنَّى، حَدَّثَنَا عَبْدُ الرَّحْمَنِ، حَدَّثَنَا سُفْيَانُ، عَنْ إِبْرَاهِيمَ بْنِ عُقْبَةَ، عَنْ كُرَيْبٍ، أَنَّ امْرَأَةً، رَفَعَتْ صَبِيًّا فَقَالَتْ يَا رَسُولَ اللَّهِ أَلِهَذَا حَجٌّ قَالَ ‏ "‏ نَعَمْ وَلَكِ أَجْرٌ ‏"‏ ‏.‏
Reference : Sahih Muslim 1336 c
In-book reference : Book 15, Hadith 459
USC-MSA web (English) reference : Book 7, Hadith 3093
  (deprecated numbering scheme)