Deep learning (DL) reconstruction particularly of MRI has led to improvements in image fidelity and reduction of acquisition time. In neuroimaging, DL methods can reconstruct high-quality images from undersampled data. However, it is essential to consider fairness in DL algorithms, particularly in terms of demographic characteristics. This study presents the first fairness analysis in a DL-based brain MRI reconstruction model. The model utilises the U-Net architecture for image reconstruction and explores the presence and sources of unfairness by implementing baseline Empirical Risk Minimisation (ERM) and rebalancing strategies. Model performance is evaluated using image reconstruction metrics. Our findings reveal statistically significant performance biases between the gender and age subgroups. Surprisingly, data imbalance and training discrimination are not the main sources of bias. This analysis provides insights of fairness in DL-based image reconstruction and aims to improve equity in medical AI applications.