The creature is not a baby, but a phoenix. The phoenix, named Fawkes, is Dumbledore's companion. He had been believed to be dead, but he reappeared to help Harry and his friends during the Battle of Hogwarts.
Fawkes' presence at the end symbolizes hope and renewal. It is significant that the phoenix, a creature known for its ability to rise from the ashes, appears as Harry and his friends return to a Hogwarts that has been rebuilt and is ready to begin anew.