Carrying a child during الطواف is جائز and does not invalidate the الطواف of the carrier عند the consensus of scholars. النبي (صلى الله عليه 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, النبي performed الطواف while riding his camel, demonstrating that الطواف is valid even when not walking on one's own feet.
الشيخ ابن باز ruled that if a person carries a child during الطواف and intends the الطواف for both themselves and the child, it counts for both of them. He based this on the hadith of the woman who asked النبي whether her child could perform الحج, and he confirmed that the child would receive reward. The guardian performs the rites on behalf of the non-discerning child, and الطواف performed while carrying the child fulfills the الطواف requirement for both.
الشيخ ابن عثيمين added that using a baby carrier, stroller, or having someone else push the child in a wheelchair alongside the person performing الطواف are all acceptable methods. He noted that the key requirement is that the carrier completes seven full circuits around the الكعبة. The practical concern is the extreme crowding during peak times, and scholars recommend choosing less crowded times or performing الطواف on upper floors when carrying young children for their safety.