Fusarium head blight (FHB) and the accumulation of deoxynivalenol (DON) mycotoxin induced by Fusarium graminearum and other Fusarium fungi cause serious problems for oat production in the Nordic region (Scandinavia, Fennoscandia). Besides toxin accumulation, FHB causes reduction in grain yield and in germination capacity. Here, genomic approaches for accelerating breeding efforts against FHB and DON accumulation were studied. Resistance-related traits included DON content, F. graminearum DNA (relative to oat DNA) content (qFUSG) measured with real-time quantitative polymerase chain reaction (PCR), Fusarium-infected kernels (FIKs) and germination capacity (GC). Plant germplasm used in the study consisted of mostly breeding lines, and additionally, a few cultivars and exotic accessions. Genome-wide association study (GWAS) and genomic prediction, enabling genomic selection (GS) on the resistance-related and collected agronomic traits, were performed. Considerable genetic correlations between resistance-related traits were observed: DON content had a positive correlation (0.60) with qFUSG and a negative correlation (−0.63) with germination capacity. With the material in hand, we were not able to find any significant associations between markers and resistance-related traits. On the other hand, in genomic prediction, some resistance-related traits showed favorable accuracy in fivefold cross-validation (GC = 0.57). Genomic prediction is a promising method and genomic estimated breeding values (GEBVs) generated for germination capacity are applicable in oat breeding programs.