The question has been answered many times, but none so definitively as with Hippolytus.
At the hour in which the cock crows, they shall first pray over the water. When they come to the water, the water shall be pure and flowing, that is, the water of a spring or a flowing body of water.
Then they shall take off all their clothes.The children shall be baptized first. All of the children who can answer for themselves, let them answer. If there are any children who cannot answer for themselves, let their parents answer for them, or someone else from their family.
After this, the men will be baptized. Finally, the women, after they have unbound their hair, and removed their jewelry. No one shall take any foreign object with themselves down into the water…
Hippolytus of Rome (d. 235), The Apostolic Tradition
