I second the resume thing. I have moved 4 times with Titan. he is 4 and weighs 95 lbs, so a little different in weight. It also helps if you can talk directly to the owner vs the rental company. That or hire a Realtor to find somewhere. It's getting harder and harder because it isn't so much the weight as the breed. Often it's the home owner's insurance that won't allow the dog. Unfortunately here, in NW FL, they also just don't like big dogs.
Start a resume of sorts. OB certs, letters from people that know her, previous land lords, etc. Any other proof you have that your dog isn't a threat. That will go a long way believe it or not.
Good luck, house hunting with a GSD isn't ideal at all if you aren't buying.
Commander Charly Titan (GSD)-15 Jan 2010