I have a girlfriend in Germany and she is pregnant with my child and she has one year Germany resident and she is not working yet, and the job center is paying her, and I'm from Italy and have Italian residency and I want to stay with her with my unborn baby in the same house that the government is paying for her. I want to know if there should be a problem staying with her, because she had one child before, we both are from Nigeria. Can anyone advise me how it is over there if is possible to live with her without any problem?
When you have a long term visa for Italy, you're allowed to stay for a period of no more than 90 days per half-year in the territory of other Schengen countries, in your case, Germany. Staying in her house should be no problem at all.
If you want to stay for more than 90 days, you have to apply for a long term visa for Germany.
It will not be easy to get a long term visa as your girlfriend is not working and her house is paid by the jobcenter. From Auswärtiges Amt (Federal Foreign Office):
A foreigner must have a settlement or residence permit or an EU Blue Card and sufficient living space before his/her family is allowed to join him/her. Further requirements must also be fulfilled, depending on the status of the foreigner resident in Germany.
As regards the subsequent immigration of spouses, the amended Immigration Act introduced the rule that both spouses must be 18 years or older and that the person arriving in Germany to join their spouse must in principle have at least a basic knowledge of German.