Immigration requirements for child in EU

Location: United States/ Germany

I’m a US citizen with dual citizenship via my grandparents to Ireland. As such I have an EU passport.

I’m planning to move to Germany next year. Under the freedom of movement act I won’t need a visa to move or find work in Germany.

The plot twist is that I’m also currently pregnant and will have the baby before my move. The baby will be a US citizen, and isn’t eligible for my Irish citizenship through descent.

I’m wondering what I need to do to ensure they can live with me in Germany. And how young would they be able to apply for naturalization in Germany?

Danke!