Standard classification of canine vocalisations is severely limited for assistance dogs, where sample data is sparse and variable across dogs and where capture of the full range of bark types is ethically constrained. We reframe this problem as a continuous regression task within a two-dimensional arousal-valence space. Central to our approach is an adjusted Siamese Network trained not on binary similarity, but on the ordinal and numeric distance between input sample pairs. Trained on a public dataset, our model reduces Turn-around Percentage by up to 50% on the challenging valence dimension compared to a regression baseline. Qualitative validation on a real-world dataset confirms the learned space is semantically meaningful, establishing a proof-of-concept for analysing canine barking under severe data limitations.