Gender inequality is a widespread problem in our society. It can manifest itself in many ways and contexts, and starting as early as primary school. While an increasing number of initiatives aim at tackling gender biases and inequalities, few of them are aimed at raising awareness of gender (in)equalities among young children, i.e., at the age in which such inequalities appear in their lives. The potential shown by social robots in teaching non-curricular topics is a promising motivation for exploring their use in this context. Indeed, a social robot could offer children the possibility to discuss gender (in)equality with an intelligent entity that is neither male nor female, but rather a credible outsider with respect to mankind. In this article we present the design process of a social robot, named PixelBot, and associated robot-mediated storytelling activity aimed at raising awareness of gender (in)equality among children. We used a participatory design approach involving 20 children aged 10-13 to acquire (i) their opinion on how a robot should look like and (ii) stories featuring robots and gender (in)equality. Finally, we conducted a study involving 8 children aged 9-10 to test the co-designed robot and robot-based storytelling activity. Results suggest that social robots are a promising avenue to promote gender equality and respect in children.