Pretty Polly, in my mind is always connected to owning a parrot.
Owning parrots was a common and popular thing in years gone by, the 60's and 70's maybe.
"Polly" was a very common name for a parrot, and people always said, "Pretty Polly!" of course the parrot would repeat it, because they mimic speech.
So, if you ask people what parrots say they might reply, "pretty Polly".
And it probably came from the fact that people like to use the same letter twice, so they wondered which name to call their parrot, Polly, Polly the parrot.
Pretty Polly.
Wow, the shite in my head :D
Either that or it's just a fictional character that people use because it goes well with "pretty".
As far as I know there is no pretty Polly in history.