Is it permissible for a woman whose husband has passed away to perform the Hajj pilgrimage before the end of her waiting period (four months and ten days), especially if she is elderly and may not be able to perform Hajj at a later time?

The madhhab (definition) of the majority of scholars is that a woman whose husband has passed away must reside in her deceased husband's house until her 'iddah (definition) (waiting period) ends. She is not permitted to leave it except out of necessity. They based their ruling on the hadith (definition) of Furay'ah and on the fact that 'Umar ibn al-Khattab used to send back women whose husbands had died, from al-Bayda'. Therefore, the questioner is not permitted to go for Hajj as long as her 'iddah has not ended.