Surely the king knows she put in a resignation letter already but that not enough for him to give up on her and he doesn't even know about the pregnancy. And why not get the 3 doctors papers saying she's pregnant so she can easily leave instead of being a deserter? No one knows who the father is and it would be hard to prove the king is the father until 9 months from now and even then who would believe the king met someone at a festival. She could even lie and say the father is some random guy, since she did sleep with a random guy its not really a lie