Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
We are not aware of any specific supplication or remembrance that a pregnant woman should say. However, she can say any Dua (supplication) she wishes for the good of this world and of the Hereafter.
For instance she may supplicate with what Ibn Hibban reported in his Sahih, that Anas, may Allah be pleased with him, narrated that the Prophet (Sallallahu Alaihi wa Sallam) said:ا"O Allah, there is no ease except in that which you have made easy and you make the difficult, if You wish, easy."
She can also supplicate with the verse of Allah: "Our Lord! Bestow on us from our wives and our offspring who will be the comfort of our eyes, and make us leaders for the Muttaqûn" (pious)" (Al-Furqan 25:74)
Another supplication is the one reported by Abu Dawud in his Sunan that Abu Bakrah, may Allah be pleased with him, narrated that the Prophet (Sallallahu Alaihi wa Sallam) said: "The supplication for one's distress is: O Allah, it is Your Mercy that I hope for, so do not leave me in charge of my affairs even for a blink of an eye and rectify for me all of my affairs. None has the right to be worshipped except You."
Nevertheless, the ruling of a pregnant woman does not differ from a non-pregnant woman in things that she has to do and things that she does not have to do. She has to pray, and she fasts if she does not find any difficulty in doing so, and if it does not harm her fetus and so on. However, the scholars differ about the blood that may come out of her, whether it is considered as menstruation blood or not. The preponderant opinion is that it is not menstruation; therefore it does not affect prayers or fasting. Unless this blood is discharged one day or two days before delivery and is connected with it (delivery), in this case it is considered childbirth blood and therefore she stops fasting and praying.
Allah knows best.