It would be more sane to have women traveling alone comment on this question and not a bunch of white males who have the knee jerk reaction of "go buy a gun".
With dogs the alpha aspect is an issue only if the dog is male and the owner/master is male as well. If the owner is a female the alpha dog will protect his property and do so far more aggressively than if his owner is a female. I saw it happen many times with girl friends with male dogs. A couple even chewed up my clothes to let me know they did not approve of a new male into their home. A friend would stay over at his then girl friend's (now his wife) place and her male cat would spray his pillow. It is a guy thing.
A dog is also a good companion for anyone spending a lot of time alone regardless of any protection. In most cases having an alarm dog that barks is all that is needed and little dogs tend to bark a lot more at any little noise.