Is it permissible for a woman to pray to drink from the hand of the Messenger of Allah (blessings and peace of Allah be upon him) on the Day of Resurrection?

One of the proven reports from the Prophet (blessings and
peace of Allah be upon him) states that whoever drinks from his Cistern on
the Day of Resurrection will never thirst again after that.  It was
narrated that ‘Abdullah ibn ‘Amr (may Allah be pleased with him) said: The
Prophet (blessings and peace of Allah be upon him) said: “My cistern is
the size of a month’s journey, its water is whiter than milk, its
fragrance is better than musk, and its jugs are like the stars of the sky.
Whoever drinks from it will never thirst again.”

Narrated by al-Bukhaari (6579) and Muslim (2292). 

It was narrated that Sahl ibn Sa‘d (may Allah be pleased with
him) said: I heard the Prophet (blessings and peace of Allah be upon him)
say: “I will reach the Cistern ahead of you. Whoever comes to it will drink
from it, and whoever drinks from it will never thirst again after that…”

Narrated by al-Bukhaari (7051) and Muslim (2291) 

These hadiths clearly state that whoever drinks from the
cistern of the Prophet (blessings and peace of Allah be upon him), male or
female, will never thirst again after that. 

Al-Qaadi ‘Iyaad (may Allah have mercy on him) said: The
apparent meaning of the hadith of the cistern indicates that his entire
ummah will drink from it, except those who turn back on their heels, change
(the religion) and introduce (innovations).

End quote from Ikmaal al-Mu‘allim Sharh Saheeh Muslim
(7/130) 

The apparent meaning of these hadiths indicates that the
drinking will be directly from the cistern or from the jugs that are near to
it, and that the people will drink from it themselves. 

We have not seen in any version of the hadith anything to
suggest that they will drink from the hand of the Prophet (blessings and
peace of Allah be upon him). 

If people were to drink at the cistern from the hand of the
Prophet (blessings and peace of Allah be upon him), he would have told us of
that. 

Therefore, with regard to a Muslim – male or female –praying
that Allah will give him to drink from the hand of the Messenger (blessings
and peace of Allah be upon him) an enjoyable drink after which they will
never thirst again, there is the fear that this may come under the heading
of overstepping the mark in supplication and asking Allah for something of
which we have no knowledge. 

Ibn al-Qayyim (may Allah have mercy on him) said: Any request
that is contrary to the wisdom of Allah, or implies going against His laws
and commands, or implies going against what He has told us, comes under the
heading of overstepping the mark, which Allah does not love and He does not
love the one who makes such a request.

End quote from Badaa’i‘ al-Fawaa’id (3/524) 

What is prescribed is for the Muslim to ask Allah to cause
him to drink from the cistern of the Prophet (blessings and peace of Allah
be upon him), a drink after which he will never thirst again. So he should
limit his request in his supplication to that which is mentioned in the
saheeh texts. And Allah knows best. 

Moreover, for women to drink from the hand of the Messenger
(blessings and peace of Allah be upon him) is not something prohibited,
because the Messenger (blessings and peace of Allah be upon him) is like a
father to all the believers (both men and women). Therefore one of his
unique characteristics (blessings and peace of Allah be upon him) was that
it was not haraam for him to touch a woman who was not his mahram, or to be
alone with her. 

Al-Haafiz Ibn Hajar (may Allah have mercy on him) said: 

What is clear to us, on the basis of strong evidence, is that
one of the unique characteristics of the Prophet (blessings and peace of
Allah be upon him) is that it was permissible for him to be alone with a
non-mahram woman and to look at her. This is the correct answer regarding
the story of Umm Haraam bint Milhaan, and his entering upon her, sleeping in
her house, and her combing his hair, even though there was no relationship
through ties of blood or marriage between them.

End quote from Fath al-Baari Sharh Saheeh al-Bukhaari
by Ibn Hajar (9/203).