Living near a hospital, as I do, I could tell you that I see "a nurse with a purse" passing my window a dozen times a day! My previous response was intended precisely to "expand" on the phrase in order to explain the circumstances in which it is normally used...ie the source-situation.
Since you actually seem to want an answer to the question: "Who first said 'a nurse with a purse'?"...I wish you luck in finding the answer. The language is awash with such rhyming phrases...the hostess with the mostest...meals on wheels etc. Some of these are attributable to known 'authors' but most are not, as it seems that they, like Topsy, "just growed".