After researching the matter, we have not found anything to indicate that the duaa' of a pregnant woman will be answered, either in the marfoo hadeeths (those that are attributed to the Prophet (blessings and peace of Allah be upon him)) or in mawqoof reports (those that are attributed to the Sahaabah).
But if the Muslim combines positive thinking about Allah, may He be exalted, and certainty of His generosity with proper humility before Him, then we hope that Allah will answer his du aa's and fulfil his hopes.
It remains for us to note that the duaa' of the mother for her child is one of the duaa's that will be answered, because the Prophet (blessings and peace of Allah be upon him) said: There are three duaa's that will undoubtedly be answered: the duaa' of one who has been wronged, the duaa' of the traveller and the duaa' of a father for his child.
Narrated by at-Tirmidhi (1905). See also Saheeh al-Adab al-Mufrad, 372
Al-Mannaawi (may Allah have mercy on him) said:
The duaa' of the father for his child is because he is truly compassionate towards him and often prefers him to himself. As his compassion is genuine, then his duaa' will be answered. The mother is not mentioned even though the emphasis on her rights may indicate that her duaa' is more likely to be answered than that of the father, because this is something that is well known. End quote.
Fayd al-Qadeer, 3/301
If a pregnant woman prays for her baby to be righteous, smart and of good character, then we hope that Allah will answer her prayer.
Please see also the answer to question no. 13506 for a discussion on the conditions of duaa' being answered.
And Allah knows best.
Reproduced from Islam QA