Current Grammar Error Correction (GEC) initiatives tend to focus on major languages, with less attention given to low-resource languages like Esperanto. In this article, we begin to bridge this gap by first conducting a comprehensive frequency analysis using the Eo-GP dataset, created explicitly for this purpose. We then introduce the Eo-GEC dataset, derived from authentic user cases and annotated with fine-grained linguistic details for error identification. Leveraging GPT-3.5 and GPT-4, our experiments show that GPT-4 outperforms GPT-3.5 in both automated and human evaluations, highlighting its efficacy in addressing Esperanto's grammatical peculiarities and illustrating the potential of advanced language models to enhance GEC strategies for less commonly studied languages.