I like that idea.
Unless a court has stripped him of his parental rights you will need you ex's consent or you will have to convince a judge that it is the best interest of the child. That's the tough part but you don't need a lawyer to do it.
Google Mississippi Name Change for a Minor and you'll come up with guides, forms and instructions.
If you don't succeed your daughter is not too young to learn that life can sometimes be unkind and one doesn't always get what one wants.

