All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The basic rule is that zakah Al-Fitr is obligatory on Muslim men and that he also has to give it on behalf of all those whom he is legally obligated to support such as his wife, children, and other dependants. Since your sister works and has a sufficient income, your father is no longer required to support her and, consequently, does not have to give zakah Al-Fitr on her behalf. Rather, she must give it herself, from her own property. Nevertheless, if the father pays it on her behalf from his money, then this will be sufficient to clear her of her liability, and there is no harm in that.
Allaah Knows best.