You need some genetic information, e.g. SNP markers to check for alleles either from genome sequencing or genotyping (SNP) arrays, or other easier-to-use genetic markers (inter-simple sequence repeat (ISSR)) (For dogs it is described in Kriangwanich et al. 2020). Then you also need a panel (genetic information of the different breeds to map out representative alleles for each breed) to compare the test alleles to. But it all depends on what kind of data you can produce for your samples. On SNP data you could run ADMIXTURE or STRUCTURE, and produce a phylogenetic tree.