Voice anonymization aims to protect speaker identity while preserving linguistic content and speech usability. However, most anonymization systems are developed on adult speech, leading to degraded performance when applied to child speech. This paper investigates child-centric anonymization by adapting a self-supervised learning (SSL) based anonymization pipeline to the child speech domain. The system is adapted using child speech from the MyST corpus and evaluated under both single-speaker and two-speaker mixture conditions. Experimental results show that child-domain adaptation improves intelligibility and perceptual quality while maintaining strong privacy protection. Extending the approach to multi-speaker further demonstrates that combining target speaker extraction with child-adapted anonymization provides privacy protection while preserving conversational structure. These findings highlight the importance of child-specific adaptation for practical speech anonymization systems.