Dude, it depends on your personality and looks sadly enough. A stutter shouldn't really put any nice girl off. If your a nice guy and a nice looking guy you will never have a problem finding someone. If your not nice looking, Dress well, look clean, smell nice (MAKE YOURSELF NICE LOOKING! its what I do, and it works. I've dated quite a few cute girls. Experiment with styles and looks until you find something that suits you) and you will find yourself a nice and/or pretty gal :)
If he is a nice guy and a good person and really someone you like, of course ! The inside beauty of any one him/her makes the person who they are, stuttering or things like that are just little stuff... You shouldn't be emberassed !