There's a jig called "Kitty's Rambles" / "The Rambles of Kitty" (depending on which form of the genitive case is to the fore) but this one is nothing like it, apart from having the same time signature, structure and almost the same name. I've never seen this one referred to as "The Rambles of Cat" but I have seen "Whelan's Old Sow" (but not "The Old Sow of Whelan") pinned to it.
Neither tunes' names nor names of tunes ever made much sense to me. Hopefully this cat's / Kit's / whatever you please sir's, apostrophised journey won't lead to an 'astrophe.