Praise be to Allah.
May Allaah bless you; we congratulate you for the blessing of Islam, for it is the greatest of blessings. We also congratulate you for your marriage, and we ask Allaah to continue to bless it, and to bless you with a righteous husband and righteous offspring.
If the marriage was done with the agreement of your father and in the presence of two witnesses, then it is a valid marriage, and it does not matter that the marriage contract was not written down or that the mahr (dowry) was not recorded. But the marriage contract should be written down because that helps to protect people’s rights. As your marriage was done before you became Muslim, then your wali (guardian) was your father who was of the same religion as you, so if you want to write it down and document what is in the marriage contract, there is nothing wrong with that.
But now your father is not qualified to act as your guardian, because of the difference in religion. See the answer to question no. 48992.
But you do not need a wali now, because the previous marriage contract is valid, as stated above.
And Allaah knows best.