I am pregnant and live in Texas. The father (no test has been performed yet) is not agreeable to marriage but does want to be involved in our child's life. I was involved with another man before the baby's father and he does want to marry me and be a father to my child. We would like to move to California for the next couple of years. I am unsure if there are any legal reasons I should stay in Texas if I do not desire to. What rights does the baby's father have at this point?

Until the baby is born and legal paternity is established, you are free to do whatever you choose.

There are no legal reasons for you to stay. There are moral ones, but this isn't the family morality board...

Also there is a chance that if he goes to court he can force you to return to Texas if you wanted or give up the child. The full backing of the courts may come down on you. You need to consult a lawyer before doing any such thing.