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.
We are not aware of the reality of this ceremony (Bi-yat), nonetheless, if it is truly like the Christian baptism, then it is not permissible to attend it, as baptism is among the rites of non-Muslims who associate partners to Allaah. For more benefit, please refer to Fataawa 82258 and 90151.
If your cousin is a Muslim, then you should advise him not to arrange this ceremony as the Prophet said: "The essence of religion is advice." [Muslim]
As regards this girl, you have no obligations towards her, but you should advise her parents and encourage them to do what is religiously required from them, like offer the 'Aqeeqah for her and giving her a Muslim name and the like.