Hadith: I saw the Prophet (may Allah's peace and blessings be upon him) leading people in prayer and carrying Umāmah bint Abu al-‘Ās, the daughter of the Prophet's daughter Zaynab, on his shoulder. He put her down when he wanted to bow, and he picked her up again when he got up after prostration

عن أبي قتادة الأنصاري رضي الله عنه ، قال: «رأيتُ النبيَّ صلى الله عليه وسلم يَؤُمُّ الناس وأُمَامَة بِنْت أَبِي العَاصِ وهي ابنةُ زينب بنتِ النبي صلى الله عليه وسلم على عاتِقِه، فإذا ركَع وضَعها، وإذا رفَع مِن السُّجُود أعَادَها».
[صحيح] - [متفق عليه]

Abu Qatādah al-Ansāri (may Allah be pleased with him) reported: I saw the Prophet (may Allah's peace and blessings be upon him) leading people in prayer and carrying Umāmah bint Abu al-‘Ās, the daughter of the Prophet's daughter Zaynab, on his shoulder. He put her down when he wanted to bow, and he picked her up again when he got up after prostration.
[Authentic hadith] - [Narrated by Bukhari & Muslim]

Explanation

The noble Hadīth shows that the Prophet (may Allah's peace and blessings be upon him) was leading the people in prayer while carrying Umāmah bint al-‘Ās, the daughter of his daughter Zaynab, (may Allah be pleased with her). On bowing and prostrating, he put her down, and when he stood up he carried her and so on. This indicates that there is nothing wrong with carrying children when praying.