Whilst it is disliked for Muslims to have dogs in their homes, undoubtedly the dog is not considered despised and accursed as some folks make them out to be. Dogs are God's creation and humans must never mistreat them and be merciless towards them. In fact it has been narrated in two hadiths that a man and a prostitute were forgiven for their sins simply for giving water to thirsty and dying dogs.
Dogs make great guards and fab hunters. They can also be very loyal and helpful beings. Yes there are many times they have been known to turn violent and deadly even unpredictably, but that's the case with many animals. It doesn't mean people can go about killing them and abusing them claiming its for religious reasons(yes many people do this!)
As for the OP then I agree I will feel unsafe if I see an unleashed dog going around and this is because of the numerous horror stories I've heard/read on dog attacks. The lady in question shouldn't do what she's doing as she's risking the lives of others and even her own beloved pet by her actions.