Answer
Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
1- It is haram for the person who in a state of impurity following sexual activity to perform ritual Prayer, perform Tawaf, stay in the mosque, recite or touch the Quran. Everything else is permissible.
2- However, there is nothing wrong with a person who is in a state of ritual impurity to do the household duties or any other needs.
Answering your question, we would like to quote the following fatwa published on www.islamqa.info:
There is no set time limit within which a woman who is in a state of ritual impurity has to do ghusl (major bath). It has to do with the performance of Prayers and other acts of worship where purity is required.
There is no harm in delaying ghusl until the time for the next Prayer comes. But it is recommended for the Muslim to hasten to do ghusl so that he or she will always be in a state of purity, as is the sunnah, and because the angels do not come near a person who is sexually defied.
The Prophet (peace and blessings be upon him) said: “There are three things which the angels do not approach: the dead body of a disbeliever, a man who has perfumed himself with saffron [because this is frivolous and foolish behavior and an imitation of women and a person who is sexually defiled except that he performs ablution” (Abu Dawud)
If a woman is busy and it is not easy for her to do ghusl from impurity straight after intercourse, this does not affect her and she is not impure. It is sufficient for her to do wudu’ (ablution), to reduce the impurity and so that the angels will come near her.
The claim that some people make, that it is haram for a woman who is in a state of ritual impurity to touch things and to do certain things, is all innovated (bid`ah) and false ideas which have no basis in Islam.
This false belief is based on false and fabricated hadiths that have been reported on this topic.
Sheikh Ash-Shuqairi (may Allah have mercy on him) said: Among these false ideas is the notion that if a woman who is in a state of ritual impurity kneads dough, it becomes corrupt because of her impurity, and that the blessing will vanish from everything her hand touches. (As-Sunan wal-Mubtada`at)
A similar question was submitted to the Standing Committee on Scientific Research and Fatwas. The text of their response is as follows:
Yes, it is permissible for a person—whether a man or a woman—who is in a state of ritual impurity to touch things such as clothes, plates, pots, and so on before doing ghusl because this person is not impure and does not make the things he or she touches impure.
It was reported in an authentic hadith that Abu Hurairah (may Allah be pleased with him) was with the Prophet (peace and blessings be upon him) one day; then he withdrew from him, then he came back. The Prophet (peace and blessings be upon him) said to him: “Where were you, Abu Hurairah?” He said, “I was in a state of ritual impurity and I did not want to sit with you when I was not pure.” The Prophet (peace and blessings be upon him) said, “Subhan Allah, a Muslim does not become impure” (Al-Bukhari)
Allah Almighty knows best.
Excerpted, with slight modifications from: www.islamqa.info