During the `iddah the widow has to stay in her home and, consequently, she is not allowed to travel even for Hajj, whether it is obligatory Hajj or non-obligatory.
Dr. Muzzamil Siddiq, former President of the Islamic Society of North America, states that: Immediately after the death of her husband, a widow should observe `iddah for four months and ten days. Almighty Allah says, (Such of you as die and leave behind them wives, they (the wives) shall wait, keeping themselves apart, four months and ten days. And when they reach the term (prescribed for them) then there is no sin for you in aught that they may do with themselves in decency. Allah is Informed of what ye do) (Al-Baqarah 2:234) .
In case the widow is pregnant, then her `iddah should continue until she delivers. Almighty Allah says, (And for those with child, their period shall be till they bring forth their burden) (At-Talaq 65:4). The Prophet (peace and blessings be upon him) also explained this in his Hadith reported by Imam Bukhari that reads: “It is forbidden to mourn for a dead person for more than three days, except in the case of a widow for whom mourning is allowed for four months and ten days.” (Al-Bukhari)
During that time she is not allowed to wear kohl, perfumes or put on colourful dresses. But she is allowed to wear light perfume when bathing after menses.
According to the Sunnah, a widow should spend her time at home and should not go out for socialization. She should wear plain and simple clothes and avoid perfumes and make-up. All widows, whether young or old, should observe these rules, according to the Sunnah of the Prophet (peace and blessings be upon him).
A widow, however, does not have to cover her hair all the time. When she is in her home and in front of other mahrams (close male relatives who are forbidden to marry her), then she can uncover her head. She is not required to wear black clothes or black head cover.
As for offering Hajj during the period of `iddah, Dr. Muzammil adds:
During the `iddah the widow has to stay in her home and, consequently, she is not allowed to travel even for Hajj, whether it is obligatory Hajj or non-obligatory. She has to complete the `iddah now and then she can go for Hajj. She made the intention for Hajj, and in sha’ Allah, if she is alive and healthy she can make Hajj next year, but she should not travel during the `iddah.