This study introduces a Machine Learning (ML) approach for estimating the T2 spectrum and myelin water fraction (MWF) using multi-echo T2 (MET2) data from preclinical 7T Magnetic Resonance Imaging (MRI) scanners. ML methods have shown promise in MWF estimation, outperforming Regularized Non-Negative Least Squares (RNNLS). However, existing ML methods were optimized for high signal-to-noise ratios (SNR) typical of 3T clinical MET2 data with larger voxel sizes. We adapted the Model-Informed Machine Learning (MIML) method to handle challenges in preclinical 7T MRI, including reduced voxel sizes, elevated noise levels (SNR=30-60), and shifts in T2 lobes. Results from in-silico simulated data demonstrate the superior performance of the proposed multi-layer-perceptron-based solution over RNNLS. Validation with ME T2 data from two mice - a healthy control and a cuprizone-exposed pathological mouse - confirms the ML method's success in identifying cuprizone-induced demyelination. Our study showcases the adaptability and enhanced performance of the MIML approach under challenging preclinical 7T MRI conditions, contributing to the advancement of MWF estimation methods in high-field MRI settings.