I am pregnant and I want to know what happens if I move to a different state before the baby is born in regards to her father?

The father can get a DNA test, and ask for visitation rights.

You can move anywhere you please since the child is not born, you could also do so even if the child was born and there was NO court order stating otherwise.

Regardless if you move, the father can do as Fr_Chuck said, and file for visitation... in which you would most likely be ordered to meet him halfway (in distance) for visitation... so keep that in mind.

If the father petitions for visitation then you'll have to provide the means for that to occur. He might try to prevent you from moving but it's not likely he'd be successful. The onus for traveling for court appearances, etc. would no doubt fall on you if you willingly choose to move out-of-state while pregnant.