This is typical of credobaptists, both regular and the Anabaptist variety. I cannot say what non-Christian groups observe this extra-biblical practice.
Judges 13 1And the people of Israel again did what was evil in the sight of the LORD, so the LORD gave them into the hand of the Philistines for forty years. 2There was a certain man of Zorah, of the tribe of the Danites, whose name was Manoah. And his wife was barren and had no children. 3 And the angel of the LORD appeared to the woman and said to her, "Behold, you are barren and have not borne children, but you shall conceive and bear a son. 4Therefore be careful and drink no wine or strong drink, and eat nothing unclean, 5for behold, you shall conceive and bear a son. No razor shall come upon his head, for the child shall be a Nazirite to God from the womb, and he shall begin to save Israel from the hand of the Philistines." 6Then the woman came and told her husband, "A man of God came to me, and his appearance was like the appearance of the angel of God, very awesome. I did not ask him where he was from, and he did not tell me his name, 7but he said to me, 'Behold, you shall conceive and bear a son. So then drink no wine or strong drink, and eat nothing unclean, for the child shall be a Nazirite to God from the womb to the day of his death.'"
Legend has it that Mary was dedicated to God by her parents.
You'll have to try again to demonstrate that it's an extra-Biblical practice.
Is your group a credobaptist? Does your group baptise people in the name of the Father, Son and Holy Spirit? Does it baptise infants as well?