If he gives his son a car, does he have to give the same to his daughter too?

Firstly: 

It is obligatory to treat children fairly in giving gifts,
and it is haraam to show preference to some over others, unless that is for
a legitimate reason, such as need, as is explained in the answer to question
no. 22169. 

A gift is something that a father gives as a present to his
children. As for maintenance, that depends on the child’s needs, and it is
not essential to give each one the same. Whoever is in need of maintenance
may take it, and whoever does not need it should not take it. It is well
known that maintenance of a minor is not like maintenance of a grown-up, and
the maintenance of one who is studying at the primary level is not like
maintenance of one who is studying at university, and maintenance of a girl
is not usually like maintenance of a boy. That includes maintenance with
regard to marriage – a father may give to one who is about to get married
what he does not give to one who is not about to get married. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said: If
we assume that one of them is in school and needs support with regard to his
schooling, such as books, exercise books, pens, pencils and the like, and
the other one does not read, and he is older than him but he is not in need,
if he gives to the former must he also give to the latter? 

The answer is that he does not have to, because fairness in
maintenance means giving each one what he needs.  

For example: if a male child needs a ghutrah (head cover) and
skullcap that cost one hundred riyals, and a female needs earrings that cost
one thousand riyals, what is fair? 

The answer is: What is fair is to buy the headgear worth one
hundred riyals for the boy and to buy earrings for the girl that are worth
ten times more than what he bought for the boy; this is proper. 

Another example: if one of them needs to get married and the
other does not need that, what is fair? 

The answer is that he should give to the one who needs to get
married and not to the other. Hence it is regarded as a mistake to do what
some people do, when they have married off those of their children who have
reached marriageable age, and they have younger children, so they write in
their will, “My children who are not yet married are to be married off using
one-third of my estate.” This is not permissible, because marriage comes
under the heading of meeting needs and these children have not yet reached
marriageable age, so bequeathing this wealth to them is haraam and the
bequest should not be carried out. Even for the heirs, it is not permissible
to carry out this bequest except for those who have reached puberty and are
of sound mind. If that is allowed there is nothing wrong with it with regard
to his share of the estate. End quote from al-Sharh al-Mumti’
(4/599). 

Based on that, if the car is something that you clearly need,
and you cannot afford to buy one, then this comes under the heading of
maintenance, and your father does not have to give your sister something
similar or of similar value. If you do not have any real need for it, or you
have enough money to buy a car yourself, then what your father has given you
comes under the heading of a gift, and in that case he has to treat all his
children fairly, and give the daughter half of what he gave to his son,
because fairness between them means giving them in the same manner as the
inheritance is divided, according to the more correct of the two scholarly
opinions.

And Allaah knows best.