I too had a child when I was young. And my family was not behind me as well. But I decided to keep my son, my family came around and they are all a huge part of his life.
I do not regret my decision at all. Yes it is hard, yes it is trying however it was right for me. And you will have to make the right decision for yourself.
Keep in mind - there are many orgs. Out there to help you with your decision, and they may be able to help you get into touch with other mothers your age to help your decision.
Another thing, if you have already named her, we both know what you want, do what's in your heart, yes it will be hard - but life is hard, if it was easy it wouldn't be so much fun.
Good luck
michelle