Children are permitted to perform হজ্জ and enter ইহরাম according to the consensus of scholars from all four schools of jurisprudence. নবী করীম (সাল্লাল্লাহু আলাইহি ওয়া সাল্লাম) affirmed this when a woman lifted her child during হজ্জ and asked: 'Is there হজ্জ for this one?' He replied: 'Yes, and you will have a reward.' This hadith establishes both the validity of a child's হজ্জ 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 ইহরাম on their behalf by making the intention (niyyah) and pronouncing the talbiyah for them. The guardian then performs তাওয়াফ 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 ইহরাম garments if possible and avoids ইহরাম restrictions as much as practically feasible.
However, the হজ্জ performed by a child — whether a discerning minor (mumayyiz) or a non-discerning infant — does not fulfill the obligation of the হজ্জ of Islam. All four schools agree that once the child reaches puberty, they must perform হজ্জ again if they meet the conditions of obligation (ability, means, etc.). Sheikh Ibn Uthaymeen noted that while the child's হজ্জ is a valid voluntary act of worship with reward, the ওয়াজিব হজ্জ can only be fulfilled by someone who has reached the age of legal responsibility (bulugh).