She has some money and her father does not spend on her; does she have to pay zakaah on it?

Whoever owns
the minimum amount of wealth (nisaab) and one full hijri year has passed
since acquiring it, must pay zakaah, even if he is saving that money to get
married or get medical treatment and so on, because of the general meaning
of the evidence that paying zakaah is obligatory. 

The nisaab
is the equivalent of 85 grams of gold or 595 grams of silver. 

If the
wealth that you have is equivalent to the nisaab, then you must pay zakaah
on it every time one full hijri year is completed. 

The believer
should understand that wealth belongs to Allaah, may He be exalted, and that
zakaah does not in fact decrease wealth, rather it increases it and makes it
grow, as Allaah says (interpretation of the meaning): 

“Take
Sadaqah (alms) from their wealth in order to purify them and sanctify them
with it, and invoke Allaah for them. Verily, your invocations are a source
of security for them; and Allaah is All-Hearer, All-Knower”

[al-Tawbah 9:103]

And the
Prophet (peace and blessings of Allaah be upon him) said: “Charity does
not decrease wealth.” Narrated by Muslim (2588). 

How many
people have wealth but never enjoy it, and how many generous givers have
been blessed by Allaah with the little they have. 

Charity is
also a means of being healed of sickness, as the Prophet (peace and
blessings of Allaah be upon him) said: “Treat your sick ones with charity.”
Classed as hasan by al-Albaani in Saheeh al-Jaami’ (3358). 

We ask
Allaah to heal you and bless your wealth for you. 

And Allaah
knows best.