Legal Question in Family Law in Kentucky

No, there is no law against it.

However, your daughter has two parents. Therefore, if her father objects to you moving away with the child, you might have a custody battle on your hands. Child custody in Kentucky is determined on the basis of the "best interests of the child," which is statutory (KRS 403.270). Therefore, if asked to make a decision about custody, the court will review the facts of the case and apply that standard.

I would recommend working out a custody agreement with the father before committing to the move. Depending on your county, there are guidelines for long distance timesharing. Find an attorney in your area who can draft one for you, and if you cannot afford an attorney, contact your local Legal Aid office or your local bar association for pro bono or reduced fee services.