Is it permissible for a pregnant woman to perform the rituals of 'Umrah and Hajj, and does the duration of the pregnancy affect that, such as being in the fourth or eighth month, taking into consideration the possibility of miscarriage or illness due to overcrowding?

A pregnant woman is pure (tahir) and her Hajj is valid. Asma bint Umays performed Hajj with the Prophet, peace and blessings be upon him, while she was pregnant and gave birth at the Miqat. A menstruating woman (ha'id) and a woman in post-natal bleeding (nufasa) perform all the rituals of Hajj except for the circumambulation (Tawaf) and its two rak'ahs of prayer. If she has not performed the Hajj al-Islam, pregnancy is not an excuse, and she can avoid crowded areas or delegate (appoint someone to perform Tawaf on her behalf, if necessary and permissible in certain situations). However, if a trustworthy doctor determines that her going out poses a danger to her or her fetus, then she is prevented from performing Hajj that year. Some doctors differentiate between the beginning and the end of the pregnancy.