Welsh "rarebit" is a relatively recent variant. Rabbit is the original,
and it's a sort of slur on the Welsh, implying that these people are
stupid or poverty-stricken or deceptive that they melt cheese on
toast and call it rabbit.

The Welshman's dishonest, he cheats when he can,
He's little and dark, more monkey than man!
He works underground with a lamp on his hat
And sings far too loud, far too often, and flat!
[Flanders and Swann]

Terms of this ilk include Scotch woodcock (eggs
on toast), French horn, and Chinese fire drill.