Continuity mistake: In this episode Rose says her cat Fluffy died (as a lie) and Dorothy says "Rose, you've never had a cat, you're allergic." When Blanche and Rose first meet she is holding a cat named Mr. Peepers, and looking for a place she and the cat can live. Another episode she says she had a cat named Lindstrom Lindstrom.
Suggested correction: After first meeting Blanche at the supermarket, Rose gave Mr. Peepers to a boy there. Dorothy could actually mean that Rose has never owned a cat for as long as Dorothy has known her. Regarding the allergies, people can be allergic to some cats, but not others. Or they will choose to live with a cat despite the allergies.
In another episode, Rose mentions her dog Rusty saved the family cat from a fire so she definitely lived with a cat for longer.