It's her kid. Basdia wanted to have a kid with Van but he isn't old enough so they can't yet. Even so, she still hasn't given up. As to how she got pregnant, female ghouls stop aging after they finally mate. From what I recall, she had a partner before meeting Van, but since it's very difficult for ghouls to get pregnant due to their egg and sperm dying faster (perhaps due to the blessing of their god of death), her partner died before they successfully had a kid. After that, Basdia focused on being a hunter instead while thinking her body isn't fit to bear children. After meeting Van, she becomes pregnant because Van revives her old dead fertilized egg with his magic. So, no, it's unfortunately not Van's kid. But it's official that Basdia loves Van and is part of his harem.