In the DS-260 Online Form in the Petitioner is my section I selected OTHER Petitioner is my FATHER Organization Name DOES NOT APPLY so am I correct?

Yes, you are correct. In the DS-260 form, if your petitioner is your father and there is no organization involved, selecting "Other" for the petitioner and indicating that the organization name does not apply is appropriate. Just ensure that you provide all necessary details about your father in the relevant sections.