Thank you for raising your question to the Wefugee Community!
I am not too familiar with the law on freedom of movement for EU-citizens, but as far as I know and according to this overview, if your girlfriend would work for a minimum of 5-6 hours per week, this might already be sufficient to get the additional social money from the jobcenter again.
I would recommend her to apply for a Kitaplatz (daycare) already, which is anyway quite hard in Germany due to the shortage and long waiting lists. In the meantime she might manage to find somebody who is taking care of the child for a couple of hours per week.
However I can also recommend to seek some individual support in, for example, a counselling centre for migrants. I am sure there will also be one close to your place.
I hope this helps and all the best,