Welcome tot the Wefugees Community and thank you for reaching out to us.
Unfortunately, I am not an expert on the EU/Freedom of movement laws. But my colleague Éanna answered a similar question here before. I am afraid that we can not give a yes or no answer here (as we also don't have the full picture of your case). But as far as I understand (and based on the information you shared), you may be able to obtain a resident permit as family member of an EU citizen. If your girlfriend actually meets the criteria for the freedom of movement (and subsequently your child), can be assessed in detail i.e. at a migration counselling office (as it can get quite complicated).
Do you agree dear @mbeon-Éanna?
In any case, please don't hesitate to get back to us with any further questions.
All the best,