From Celtic Cookery by Iris Price Jones.
"Welsh Rabbit is probably a joke name that has become refined to Welsh Rarebit. Lady Llanover's Welsh rabbit consisted simply of toasted cheese on toast. It was the one recipe in her book, Good Cookery, which was written in Welsh."
(Aristocratic landowners had rights to the meat from the rabbits in the fields, so the rest of the people had no meat from the rabbit, and probably little meat at all. Welsh migration to the States, Canada, Patagonia, Australia, and New Zealand was partly a result of poor living conditions where they came from.)