For years, people on the street have crooned over Haileigh, dressed in classic Diane Von Furstenberg-style wrap dresses and fitted. She accessorizes with oversized shades and cross-body purses, making her look like an adult in a child’s body. So Ms. Vasquez began posting pictures of her then three-year-old to Instagram. Four years later, Haileigh has 129,000 followers. The social media posts have turned her into a child model, an aspiring actress and an Instagram star.