Children are permitted to perform الحج and enter الإحرام عند the consensus of scholars from all four schools of jurisprudence. النبي (صلى الله عليه وسلم) affirmed this when a woman lifted her child during الحج and asked: 'Is there الحج for this one?' He replied: 'Yes, and you will have a reward.' This hadith establishes both the validity of a child's الحج and the reward earned by the parent or guardian who facilitates it.
For infants and very young children who cannot understand or act for themselves, the guardian (parent or wali) enters الإحرام on their behalf by making the intention (niyyah) and pronouncing the talbiyah for them. The guardian then performs الطواف and السعي while carrying the child, and throws the pebbles on the child's behalf during the stoning ritual. الشيخ ابن باز explained that the guardian should ensure the child wears الإحرام garments if possible and avoids الإحرام restrictions as much as practically feasible.
However, the الحج performed by a child — whether a discerning minor (mumayyiz) or a non-discerning infant — does not fulfill the obligation of the الحج of Islam. All four schools agree that once the child reaches puberty, they must perform الحج again if they meet the conditions of obligation (ability, means, etc.). الشيخ ابن عثيمين noted that while the child's الحج is a valid voluntary act of worship with reward, the واجب الحج can only be fulfilled by someone who has reached the age of legal responsibility (bulugh).