Wife wants to get a dog, 6yo daughter is terrified of them

So my wife's been pushing hard for us to get a dog. She grew up with dogs and thinks it'd be great for our family. Problem is, our 6-year-old is absolutely petrified of them. Even small dogs freak her out.

I'm trying to find a middle ground here but every suggestion I make gets shot down. Has anyone dealt with something like this? I don't want to just say no to my wife but I also don't want to traumatize our kid. Any actual solutions that worked for you guys?