Gastrointestinal strongyle infections are a common challenge in dairy goat farming, potentially impacting animal health and milk production. We, therefore, conducted a study to evaluate the efficacy of pour-on eprinomectin (EPM) in early-lactating dairy goats naturally infected with gastrointestinal strongyles and to verify the related effects on milk yield and quality. A total of 42 pluriparous Camosciata delle Alpi goats, from two farms (F1 and F2), were involved in the trial. In each farm, the goats were divided into two groups: untreated (CONTROL) or treated (EPM, 1 mg/kg BW). Following the treatment, faeces were individually collected weekly for one month, subjected to copromicroscopic analysis, a faecal egg count reduction (FECR) test, and coproculture; according to the same time schedule, individual milk yield was recorded, and individual milk samples were collected and analysed (fat, protein, lactose, and somatic cell count). Data were statistically analysed by a mixed-model procedure for repeated measures over time. The low efficacy of EPM was demonstrated at all experimental times; overall FECR percentages (90% CI lower and upper bounds) were 39.00% (30.12–50.53) for F1 and 38.82% (30.08–50.10) for F2. Coprocultures allowed the identification of larvae of the genera Haemonchus, Teladorsagia, and Trichostrongylus. Goats treated with EPM showed a lower prevalence of Teladorsagia and Trichostrongylus larvae, and higher prevalence of Haemonchus larvae, compared with CONTROL goats (p < 0.001). The treatment did not significantly improve milk yield or overall milk composition.