Traditional depression screening methods, such as the PHQ-9, are particularly challenging for children in pediatric primary care due to practical limitations. AI has the potential to help, but the scarcity of annotated datasets in mental health, combined with the computational costs of training, highlights the need for efficient, zero-shot approaches. In this work, we investigate the feasibility of state-of-the-art LLMs for depressive symptom extraction in pediatric settings (ages 6-24). This approach aims to complement traditional screening and minimize diagnostic errors. Our findings show that all LLMs are 60% more efficient than word match, with Flan leading in precision (average F1: 0.65, precision: 0.78), excelling in the extraction of more rare symptoms like "sleep problems" (F1: 0.92) and "self-loathing" (F1: 0.8). Phi strikes a balance between precision (0.44) and recall (0.60), performing well in categories like "Feeling depressed" (0.69) and "Weight change" (0.78). Llama 3, with the highest recall (0.90), overgeneralizes symptoms, making it less suitable for this type of analysis. Challenges include the complexity of clinical notes and overgeneralization from PHQ-9 scores. The main challenges faced by LLMs include navigating the complex structure of clinical notes with content from different times in the patient trajectory, as well as misinterpreting elevated PHQ-9 scores. We finally demonstrate the utility of symptom annotations provided by Flan as features in an ML algorithm, which differentiates depression cases from controls with high precision of 0.78, showing a major performance boost compared to a baseline that does not use these features.