Carrying a child during طواف is permissible and does not invalidate the طواف of the carrier according to the consensus of scholars. نبی کریم (صلی اللہ علیہ وسلم) himself prayed while carrying his granddaughter Umamah bint Zaynab, setting her down when he prostrated and picking her up when he stood. This establishes that carrying a child during acts of worship does not invalidate them. Furthermore, نبی کریم performed طواف while riding his camel, demonstrating that طواف is valid even when not walking on one's own feet.
Sheikh Ibn Baz ruled that if a person carries a child during طواف and intends the طواف for both themselves and the child, it counts for both of them. He based this on the hadith of the woman who asked نبی کریم whether her child could perform حج, and he confirmed that the child would receive reward. The guardian performs the rites on behalf of the non-discerning child, and طواف performed while carrying the child fulfills the طواف requirement for both.
Sheikh Ibn Uthaymeen added that using a baby carrier, stroller, or having someone else push the child in a wheelchair alongside the person performing طواف are all acceptable methods. He noted that the key requirement is that the carrier completes seven full circuits around the کعبۃ اللہ. The practical concern is the extreme crowding during peak times, and scholars recommend choosing less crowded times or performing طواف on upper floors when carrying young children for their safety.