Toddler?
Where did you get that mistaken information?
Matthew 2:8, 10, 11, 13, 14 “young child”
Matthew 2:7 Then Herod, when he had privily called the wise men, inquired of them diligently what time the star appeared.
Matthew 2:16 - Herod kills all “from two years old and under, according to the time which he had diligently inquired of the wise men.”
Seems to me the wise men told Herod that the star appeared around two years earlier. Toddler could be the description.
Luke 2:12 Baby is βρέφος brephos which means a new-born child, an infant, a babe.
Matthew 2:8 Child is παιδίον paidion which means a young child, a little boy.
Further in Luke the Magi are not referenced when the shepherds were called. In Matthew, the Magi came 'after' Jesus was born, having related to Herod that they saw His star in the East. They set upon their journey (most likely from Persepolis or another city in Persia) which would have taken several months.
Finally, Herod dictated the death of all male children 2 years old and younger.