Can You Do Hajj While Pregnant?
Question

Is it halal for a pregnant woman to perform ‘umrah or hajj? Does it depend on the stage of pregnancy she is at (e.g. 4 months pregnant compared to 8 months pregnant)? There is risk of falling and disease due to the crowds of pilgrims?
Praise be to Allah.Hajj during pregnancy
There is no reason why a pregnant woman should not perform Hajj. A pregnant woman is tahir (pure), she has to pray and fast, and if she is divorced by talaq, her divorce is acceptable according to the Sunnah. 
It is narrated in the Sunnah that Asma bint ‘Umays (may Allah be pleased with her) went out for Hajj with the Prophet (peace and blessings of Allah be upon him) when she was pregnant and approaching full term, and she gave birth at the miqat. 
‘Aishah (may Allah be pleased with her) said: “Asma bint ‘Umays – the wife of Abu Bakr – gave birth to Muhammad ibn Abi Bakr in Shajarah and the Messenger of Allah (peace and blessings of Allah be upon him) told Abu Bakr to tell her to do ghusl and enter ihram. (Narrated by Muslim, 1209)
Shajarah refers to Dhu’l-Hulayfah, i.e., the miqat from which the people of Madinah enter ihram. 
Al-Nawawi said, concerning what we learn from this hadith: 
“This indicates that the ihram of women who are bleeding following childbirth or who are menstruating is valid and that it is mustahabb for them to do ghusl before entering ihram. There is scholarly consensus that it is obligatory, but our view and that of Malik, Abu Hanifah and the majority of scholars is that it is mustahabb. Al-Hasan and the Zahiri madhhab said that it is obligatory. 
All the actions of Hajj on the part of women who are bleeding following childbirth or who are menstruating are valid, apart from Tawaf and the two rak’ahs following tawaf, because the Prophet (peace and blessings of Allah be upon him) said: “Do what the pilgrims do but do not do tawaf.” (Sharh Muslim, 8/133)
Hajj rituals that a pregnant woman can’t do
If a woman has not yet done the obligatory Hajj, then pregnancy is not an excuse for her not to do Hajj, because she can avoid the places where there is too much crowding and pushing and shoving. If she is unable to stone the Jamarat herself, she can delegate someone to do so on her behalf. If she cannot do tawaf and sa’i, then she can do so in a wheelchair, and so on. 
Many people manage to do Hajj in comfort without any hardship. 
When going to Hajj poses a risk to a pregnant woman, can she go?
If a woman is pregnant and trustworthy doctors tell her that going for Hajj will pose a risk to her or her baby because she is sick or weak or for some other reason, then she should be prevented from doing Hajj that year. This is indicated by the words of the Prophet (peace and blessings of Allah be upon him), “There should be no harming nor reciprocating harm.” (Narrated by Ibn Majah, 2340; this is a hasan hadith. For details of its isnad, please see Jami’ al-‘Uloom wa’l-Hikam by Ibn Rajab, 1/302) 
Some doctors differentiate between early pregnancy, when there may be a risk to the foetus, and late pregnancy when such fears are groundless. 
For more about Hajj issues related to women, please see these answers: 9370 , 34380 , 36619 , 20045 .
And Allah knows best.