Would you consider "Deafness" a special needs pup ?

I've never seen anything on Rover about surcharges or higher rates for special needs dogs so it really doesn't make a difference. But, in answer to your question, the dog would be considered special needs.

BTW, I would think any responsible owner would inform you of his/her dog's special needs to make sure that you can handle it. I had someone contact me saying that their dog had severe arthritis and couldn't walk up stairs. Well, there are 14 stairs to my front door. Given that I already have a vision-impaired dog, there would be no way I could carry that dog up and down the stairs 3-4x a day. So I told her she should look for another sitter.