Is that how young Mary canonically was

It's never explicitly specified but:

While the Bible does not state Mary’s exact age, most historians and biblical scholars agree on a likely range based on cultural context.

Mary was most likely between 12 and 16 years old when Jesus was born.

This estimate comes from:

• Jewish marriage customs of the first century
• The typical age of betrothal for girls
• The timeline between engagement and childbirth

In that culture, girls were often engaged shortly after puberty and married soon after. Since Mary was already betrothed when the angel Gabriel appeared, it strongly supports the idea that she was in her early teens.

Source