thank you for your question.
In short: Yes it is possible for you to get married here in Germany. You need to get in contact with Standesamt (registry office) and hand in your and your fiancés documents they require. A passport issued by your home country is mandatory for this.
We had a few questions similar to yours here on the platform quite recently. Please check out the information provided over there (some of them might not be directly related to the situation you’re in, but it’s good to keep these things in mind):
As for your girlfriends papers, she can come to Germany for a visit and you both go to the Standesamt for a first consultation(you have to do that) if you both do not speak well German you have to take a translator with you.
Then they will let you both know what is needed for a marriage in Germany, in your particular situation.
After that you apply for family unification at the Ausländerbehörde.
I hope we could help you, if you need further assistance please do not hesitate to contact the community.