Children are permitted to perform حج and enter احرام according to the consensus of scholars from all four schools of jurisprudence. نبی کریم (صلی اللہ علیہ وسلم) affirmed this when a woman lifted her child during حج and asked: 'Is there حج for this one?' He replied: 'Yes, and you will have a reward.' This hadith establishes both the validity of a child's حج 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 احرام on their behalf by making the intention (niyyah) and pronouncing the talbiyah for them. The guardian then performs طواف and sa'i while carrying the child, and throws the pebbles on the child's behalf during the stoning ritual. Sheikh Ibn Baz explained that the guardian should ensure the child wears احرام garments if possible and avoids احرام restrictions as much as practically feasible.
However, the حج performed by a child — whether a discerning minor (mumayyiz) or a non-discerning infant — does not fulfill the obligation of the حج of Islam. All four schools agree that once the child reaches puberty, they must perform حج again if they meet the conditions of obligation (ability, means, etc.). Sheikh Ibn Uthaymeen noted that while the child's حج is a valid voluntary act of worship with reward, the واجب حج can only be fulfilled by someone who has reached the age of legal responsibility (bulugh).