The initial years of a child's life play a crucial role in gender development, establishing the foundation for subsequent experiences and choices. As a predominant platform for children, YouTube has substantial influence over how young males and females perceive and engage with the world. This research investigates the prevalence of social biases and stereotyping in children's videos across the top 100 popular YouTube Kids (YTK) channels, encompassing over 48,000 videos. Using video transcripts and video picture frames, we examine gender stereotypes in both language and visuals. Popular language-based gender bias estimation methods, including the Word Embedding Association Test (WEAT), reveal distinct gender biases in occupations children aspire to and core educational subjects like mathematics and science. Videos from non-animated YTK channels exhibit stronger correlations with societal biases than animated videos. Within the visual medium, we again identify significant gender disparities, with women underrepresented in videos discussing many occupations. Color-related stereotyping manifests in females' predominance in `pink' attire, and gender stereotyping extends to emotional expressions, with females smiling more often than males. The experience of gender stereotyping and sexism is known to affect the development of children's abilities and preferences. Therefore, the study's findings raise important concerns, highlighting a need for more regulations in creating and recommending kids' content.