the Bunny Hug Rag, not to be confused with.... 1913: Bunny Hug Rag (no 'the') by George L. Cobb (shown left). The bunny hug was one of a number of animal dances that the 'crazy kids' were doing those days.
These days, of course, the term has a different meaning. It started off fairly specific: 1990s: "bunny-hugger [n] ... an environmentalist, esp. an anti-blood sport campaigner." And then became more general: "...derogatory term for an animal lover", or: "slang; derogatory: a conservationist or animal lover", or: "Noun. An animal lover. Derog."
But, as is the case with many derogatory terms, they are subject to interpretation. Bunnies, as a stand in for animals in general, are pretty damn huggable. And as a gesture to express a love of animals, why not the hug? So as a blog name for a professional animal lover, it didn't seem a bad choice. I am an out and proud hugger of bunnies!