your child has right for support either in Philippine Law or British Law. I do not presume to know British laws but i believe they are among the signatories on the International Covenant on the rights of women and children.
You do not have to go international though because if you have money for that, i suggest you better use it for your child instead.
I am glad you now have a job. That is a sign that you might be able to support your child without the help of those bloody pirates. Uups, sorry.
Take good care of your child! Raise her well and show girl that she was not made out of sheer mistake or indiscretion. Meanwhile, do not pressure the pirate, uups, Captain Sparrow, to give support. Instead, pray that he will come to his senses and realize that he will miss a lot if he will not take care of someone as lovely, loving and responsible Filipina like you and a cute girl like your babe.
God bless and you can count on my prayers for you after i sign out.