Nikkolee, if you are out there, I'm sorry I haven't been able to get back to you before now, family crisis I'm afraid - sorted now.
The flat I mentioned is only going to be for rental for a very short time as the owner actually wants to sell having moved to France. I apologise if I misled you I was under the impression that it was for a really long rental and that he wanted to hold on to it. Again I can only apologise for my error, and wish you luck in your search. Edinburgh isn't such a big city and is easy to get around on foot, with plenty of green spaces to walk a puppy and a good bus system so try not to limit yourself to the city centre only