Small data in materials present significant challenges to constructing highly accurate machine learning models, severely hindering the widespread implementation of data-driven materials intelligent design. In this study, the Dual-Strategy Materials Intelligent Design Framework (DSMID) is introduced, which integrates two innovative methods. The Adversarial domain Adaptive Embedding Generative network (AAEG) transfers data between related property datasets, even with only 90 data points, enhancing material composition characterization and improving property prediction. Additionally, to address the challenge of screening and evaluating numerous alloy designs, the Automated Material Screening and Evaluation Pipeline (AMSEP) is implemented. This pipeline utilizes large language models with extensive domain knowledge to efficiently identify promising experimental candidates through self-retrieval and self-summarization. Experimental findings demonstrate that this approach effectively identifies and prepares new eutectic High Entropy Alloy (EHEA), notably Al14(CoCrFe)19Ni28, achieving an ultimate tensile strength of 1085 MPa and 24% elongation without heat treatment or extra processing. This demonstrates significantly greater plasticity and equivalent strength compared to the typical as-cast eutectic HEA AlCoCrFeNi2.1. The DSMID framework, combining AAEG and AMSEP, addresses the challenges of small data modeling and extensive candidate screening, contributing to cost reduction and enhanced efficiency of material design. This framework offers a promising avenue for intelligent material design, particularly in scenarios constrained by limited data availability.