Ugghhhh——plenty of feral pigs around to slaughter before i want to start eating rodents. Maybe rabbit being the only exception.
Squirrel is delicious but benefits by marinading, cuy is more tender.
Wiki says: ‘....Members of non-rodent orders, such as Chiroptera (bats), Scandentia (treeshrews), Soricomorpha (shrews and moles), Lagomorpha (hares, rabbits and pikas) and mustelid carnivores such as weasels and mink, are sometimes confused with rodents....” which means rabbits are even further removed from being rat relatives than you imagined. Just catching up on these critters they seem to have originated in North America where the greater number of rabbit species as well as rabbits still reside.
Rabbits are not rodents, although they do carry similar diseases. I'm thinking something like leporidae?