I have, in the past, found many kinds of sick/injured animals and rehabed them. I haven’t had any experience with birds, but I have always found that a call to your vet is a good place to start. If you don’t have a family vet, any vet will do. As far as diseases go, does the dove have any symptoms of illness? I would try not to handle it until you know for certain that it isn’t carrying something that could infect you.
As far as animal control goes, I am always a little wary of calling them. I know they do many good things, but the idea that they may put an animal to sleep if rehab is too much trouble makes me very sad.