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A Welch rabbit; bread and cheese toasted, i.e. a Welch rare bit. Rabbits were also a sort of wooden canns to drink out of, now out of use.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
Rabbit CatcherNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes
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Francis Grose was independently wealthy, having inherited money from his father, a jeweller. Finding himself overspending, he published a number of books; his Provincial Glossary seems to have been the starting-point for the Vulgar Tongue reproduced here.