Welcome to NeuroTalk.
I don't know how to answer that question but I hope you'll be able to keep your pet. When my dad was in the hospital with end of life care, the nurses bent the rules to let us bring his cat in for a visit (through the back stairwell).
I don't think that dogs pose as much of an allergy risk. If your dog is quiet, there might be a way to work around this? Why would the size of the dog matter that much?
Make sure you're a model tenant in every other way just to pave the way to success with this.
Someone else here might have some tips to help you keep your pet. Good luck. I hope it works in your favor. Our pets are so important for so many reasons.