You certainly can write your own petition, but it is better to consult with a local attorney to make sure your petition contains sufficient facts in support of your request for full custody.
You may need to clarify your question. It is not clear how you could have "full paternal rights" of your own daughter when you are talking about "writing" (filing?) a petition "against the father." If you are the mother, you may mean "parental" rights instead of "paternal" rights. If you are the father, and your paternity has been established, then you do have the right to petition for custody, but it would be wise for you to hire an attorney to represent you.
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