She does not have any wealth; can she take money from her father in order to do Hajj? Can she delegate someone to perform Hajj on her behalf if she is not able to do Hajj?

Praise
be to Allah

Firstly:

Hajj is
obligatory upon the adult, on condition that he or she is able to do it,
whether that adult is a man or a woman, because Allah, may He be exalted,
says (interpretation of the meaning):

“And
Hajj (pilgrimage to Makkah) to the House (Ka‘bah) is a duty that mankind
owes to Allaah, those who can afford the expenses (for one’s conveyance,
provision and residence)”

[Aal ‘Imraan
3:97].

The verse is
general in meaning and indicates that Hajj is obligatory upon the one who is
able to do it, whether that person is a man or a woman.

An- Nawawi (may
Allah have mercy on him) said: The scholars are unanimously agreed that Hajj
is obligatory upon a woman if she is able to do it.

End quote from
Sharh Muslim by an-Nawawi (4/148)

Based on that:

There is no
specific age for Hajj. If a person has reached the age of accountability and
is able to do Hajj in financial and physical terms, then he must do Hajj
immediately. For more information, please see the answer to question no.
41702.

See also the
answer to question no. 20045 and
41957.

In addition to
the conditions of being able to do Hajj, in the case of a woman it is
stipulated that she should have a mahram with her. If a woman cannot find a
mahram to do Hajj with her, then in that case she is not obliged to do Hajj,
even if she is financially and physically able. For more information, please
see the answer to question no. 83762.

Secondly:

A child is not
required to ask his or her father for money in order to perform Hajj, but if
the father chooses to give him or her money for Hajj, there is nothing wrong
with accepting it and doing Hajj with that money. Similarly, if the father
makes a booking for one of his children in a Hajj group, and pays for those
expenses, then this is something good and comes under the heading of
spending that is prescribed in Islam, and there is nothing wrong with the
child accepting such an offer, especially if the child did not ask for it.

Shaykh Ibn
‘Uthaymeen (may Allah have mercy on him) was asked:

I am a student
who has reached adulthood, and I do not have any wealth of my own. Can I ask
my father for money in order to do Hajj now, or should I wait until I
graduate and find work, so that I can do Hajj with my own money, even though
that will take a long time?

He (may Allah
have mercy on him) replied: Hajj is not obligatory for a person if he does
not have any wealth, even if his father is rich, and he does not have to ask
his father to give him money so that he can do Hajj. Rather the scholars
say: Even if your father gives you money with which to do Hajj, you are not
obliged to accept it; you can refuse and say: I do not want to do Hajj yet,
and Hajj is not obligatory upon me (at present).

Some of the
scholars say: If someone – a father or a full brother – gives you wealth
with which to do Hajj, then you must accept it and do Hajj with it.

But if someone
else gives you the money, and you fear that one day he will remind you of
his favour, then in that case you do not have to accept it and do Hajj with
it. This view is the correct one.

End quote from
Majmoo‘ Fataawa Ibn ‘Uthaymeen (21/94).

For more
information, please see the answer to question no. 3463.

Thirdly:

With regard to
appointing someone else to do Hajj on one’s behalf, this is only applicable
in the case of one who is physically unable to do Hajj because of old age or
sickness from which there is no hope of recovery. In this case what is
prescribed is to appoint someone to do Hajj on one’s behalf, if one has
wealth.

But in the case
of one who is physically able but does not have wealth, or if a woman is
financially and physically able to do Hajj, but she does not have a mahram
who can do Hajj with her, then in this case appointing someone to do it on
her behalf is not valid, because Hajj is not obligatory in the first place
in these two cases, and because a woman may be able to find someone among
her mahrams who can do Hajj with her in the future.

It says in
Majmoo‘ Fataawa Ibn Baaz (16/122):

It is not valid
to appoint someone to do Hajj on behalf of someone who is physically
healthy, even if he is poor, whether that Hajj is obligatory or
supererogatory. As for the one who is unable to do Hajj because of old age
or sickness from which there is no hope of recovery, then he must appoint
someone to do the obligatory Hajj and obligatory ‘umrah on his behalf, if he
can afford to do so, because of the general meaning of the verse in which
Allah, may He be glorified, says (interpretation of the meaning):

“And
Hajj (pilgrimage to Makkah) to the House (Ka‘bah) is a duty that mankind
owes to Allaah, those who can afford the expenses (for one’s conveyance,
provision and residence)”

[Aal ‘Imraan
3:97].

End quote.

For more
information on the rulings and guidelines on appointing someone to perform
Hajj on one’s behalf, please see the answer to question
111794.

And Allah knows
best.