Studio or 1BR needed for $1350 or less (preferably less!)

Hi,
I'm looking for a studio or 1BR in Boerum Hill, Carroll Gardens, Gowanus, Prospect Park South or Lefferts Gardens. Must be big enough to fit a king sized bed. And must be pet-friendly (I have a very well-behaved 27lb dog who never barks).
I'm a great tenant--very responsible, quiet, and I'm a non-smoker. I have excellent credit. I'm a part-time grad student but I make a very good income. I can provide a guarantor if necessary. Just looking for a nice situation, something safe and close to transportation.
Please contact me if you know of anything! Thanks!