You will probably have to get your daughter's father to take a paternity test - unless you were legally married at the time you became pregnant. Getting a paternity test from someone who does not want to be a father can take a long time. Other things to consider:
If he own's up to his responsibility he may want visitation. Can you trust him to take good care of the child during visitation?
Will he make a commitment or just come and go in and out of her life when it is convenient for him?
Is there any possibility that your fiance will want to adopt her once you are married?
Depending on the answers to these questions you may not want to fool with trying to get child support. You may want to make sure that he can't sue you for custody of this child at a later date when he decides it would be cool to be daddy.
I have had some friends who have fought for years for child support and never get anywhere when 10 -11 years later the father decides that he wouldn't have to be bothered with this if he had custody.
It would be nice if he would be the father that she needs, but he's not. Congratulations for making the decision to go to school. I know that this time in your life is very tough. Parenting is the hardest thing to do.