I have to agree with the other ladies in using your money to set yourself up at the moment over a trip for your DD to meet her father whom she probably wont be interested in until she is much older anyhow. If he is doing the same thing then thats another story. Regardless of how poor he is he could make some financial contribution to help you get over there with your DD. I wouldn't be making all the effort if he wants to meet her he would be helping more then just verbally saying her wants her over there and leaving the financial costs all to you.
The fact your so concerned about giving your daughter what you feel is essential (a relationship with her father) shows how you want to protect her and provide for her. You maybe struggling now but it doesn't mean you will be in another few years. Anything can happen and you don't know what life has install for you. I was a single mum when I was 17 and so poor but now I am financially secure. I not only had no money but her father who didn't live that far away didn't want anything to do with her. What I am saying is what maybe a huge expense now might be less of a financial difficulty in a few years time. If you use this money you have saved what does it mean you miss out on instead? The money could go towards setting up home, a car, eduaction, deposit for an investment, house etc all things that would benefit your DD as much if not more then meeting her Dad. She can still have a good relationship with him as she gets older and can use technology to keep in touch as Lulu suggested. Other then pictures as proof she has met him she will not remember a thing at the age she will be.