Ballet, a mainstream performing art predominantly associated with women, exhibits significant gender imbalances in leading positions. However, the collaboration's structural composition on gender representation in the field remains unexplored. Our study investigates the gendered labor force composition and collaboration patterns in ballet creations. Our findings reveal gender disparities in ballet creations aligned with gendered collaboration patterns and women occupying more peripheral network positions respect to men. Productivity disparities show women accessing 20-25\% of ballet creations compared to men. Mathematically derived perception errors show the underestimation of women artists' representation within ballet collaboration networks, potentially impacting women's careers in the field. Our study highlights the structural disadvantages that women face in ballet and emphasizes the need for a more inclusive and equal professional environment to improve the career development of women in the ballet industry. These insights contribute to a broader understanding of structural gender imbalances in artistic domains and can inform cultural organizations about potential affirmative actions towards a better representation of women leaders in ballet.