If my niece is having a baby but she wants me to have full custody, what do I need to do?

It is a good sign of responsibility that your neice would like you to have custody of her child, especially if she is not in a position to care for the child herself.  For you to get full, legal custody, the two of you would need to wait until after the child is born to file what is called a "Suit affecting parent-child relationship" in Texas.  It is also referred to as a SAPCR.  The suit will officially declare who the parents of the child are.  If everyone is in agreement, then you can proceed to have the judge enter final orders which grant you full custody of the child. The caveat here is that everyone, including the father, must be in agreement.  Even though your niece likes the idea, you and her will still need the cooperation of dad.  If your niece cannot care for the child, the father could ask the court for the opportunity to raise his child.  If dad has no interest in the child (mainly paying child support), then getting his consent to the order shouldn't be hard.

You and your niece need to consult with a family law attorney to have a custody order signed by her. Once done, a petition with the court where the niece resides needs to be filed so that a court order confirming your custody is approved by the court with a filed order.