Search engines in e-commerce settings allow users to search, browse, and select items from a wide range of products available online including children's items. Children's products such as toys, books, and learning materials often have stereotype-based gender associations. Both academic research and public campaigns are working to promote stereotype-free childhood development. However, to date, e-commerce search engines have not received as much attention as physical stores, product design, or marketing as a potential channel of gender stereotypes. To fill this gap, in this paper, we study the manifestations of gender stereotypes in e-commerce sites when responding to queries related to children's products by exploring query suggestions and search results. We have three primary contributions. First, we provide an aggregated list of children's products with associated gender stereotypes from the existing body of research. Second, we provide preliminary methods for identifying and quantifying gender stereotypes in system's responses. Third, to show the importance of attending this problem, we identify the existence of gender stereotypes in query suggestions and search results across multiple e-commerce sites.