Is prayer valid when performed in the clothing of a child?

Primary text

Prayer is permissible in the clothing of a child unless one is certain of its impurity. This position is held by Al-Thawri, Al-Shafi'i, and the companions of Al-Ra'y (the Hanafi school). The evidence for this is the narration by Abu Qatadah that the Prophet, peace be upon him, prayed while carrying Umamah bint Abi Al-As ibn Al-Rabi'. Furthermore, the Prophet used to pray while Al-Hasan and Al-Husayn would climb onto his back when he prostrated.