Maybe you can use these incidents to help her understand different kinds of fears and to help her learn about how to use the situation to find common ground with the other girls.
It's wonderful that your daughter knows that certain types of spiders don't really pose a threat to her or other people. Maybe she can help the other girls understand that not all spiders are a threat, and that the girls may be afraid of them because they don't know enough about them. Perhaps the other girls could help her learn the same thing about dogs. Perhaps they could all see that the fear of the dog and the fear of the spiders are actually the same kind of fear (something unknown). TBH, I think the different reactions could be wonderful for highlighting the idea that seemingly very different reactions are rooted in the same way of thinking. There's a lot to learn in there.
I understand that your DD feels isolated and unhappy. That's really hard. She's only 6 and doesn't have perspective. Why does she feel judged? I might ask her to think about how she judged others. For example, isn't she judging the other girls for being dishonest about their reactions to the spider? Why is it okay for her to be afraid of all dogs, but not okay for the other girls to be afraid of all spiders?
Again, I think there's really a lot to be learned about being afraid of all [insert animal names] and how different people react to different animals for the same reasons.
