I have been told that if you concentrate your search for housing on the actual owner of the rental property, rather than an impersonal property management company, you will have better luck.
Also, if you put together a resume of sorts for your dog, describing in detail (and with proof, such as certificates) the training you have done and the vet care you provide, you will be able to present her best paw forward to that owner when you meet them to look at the rental. If you have lived in another rental with this dog, would your landlord be open to writing a reference to include in her resume packet?
Good luck. It can be very difficult to rent with a GSD.