This paper introduces EdgeProfiler, a fast profiling framework designed for evaluating lightweight Large Language Models (LLMs) on edge systems. While LLMs offer remarkable capabilities in natural language understanding and generation, their high computational, memory, and power requirements often confine them to cloud environments. EdgeProfiler addresses these challenges by providing a systematic methodology for assessing LLM performance in resource-constrained edge settings. The framework profiles compact LLMs, including TinyLLaMA, Gemma3.1B, Llama3.2-1B, and DeepSeek-r1-1.5B, using aggressive quantization techniques and strict memory constraints. Analytical modeling is used to estimate latency, FLOPs, and energy consumption. The profiling reveals that 4-bit quantization reduces model memory usage by approximately 60-70%, while maintaining accuracy within 2-5% of full-precision baselines. Inference speeds are observed to improve by 2-3x compared to FP16 baselines across various edge devices. Power modeling estimates a 35-50% reduction in energy consumption for INT4 configurations, enabling practical deployment on hardware such as Raspberry Pi 4/5 and Jetson Orin Nano Super. Our findings emphasize the importance of efficient profiling tailored to lightweight LLMs in edge environments, balancing accuracy, energy efficiency, and computational feasibility.