I agree that this is a reasonable fear and probably one you shouldn't mind overall. That's a big A dog. Maybe she will warm up but that she is initially fearful? That makes sense. He's a huge dog. As a dog lover, I can understand. Hopefully she will begin to be less stressed by the dog over time.
You might actually have her help you feed your brother's dog and get both of them used to being around one another. Show her how to approach your brother's dog with startling it or her.
Is your brother's dog a "low-energy" dog? It may be your daughter is just a little too "hyper" for him since she has a border collie which crave action.
And you didn't state how often you visit your brother's house with or without your daughter going with you. Frequent exposure to the same dog often leads to better relationships.
Maybe the next time your brother and his family go out of town, his dog could stay over at your house so you can show your daughter just how lovable your brother's dog really is - that is provided his dog gets along with your dogs.
I think I would file this under "reasonable fears". Although you know the dog is sweet, that is an enormous dog, weighing about 6X what your daughter does. When it barks or approaches her, that would be frightening. If she continues to play happily with your other dog and doesn't generalize this fear to other dogs, I'd just call it normal.
Rather than say "why are you afraid, there's nothing to fear", (if you're saying that) a better response is, "Honey, that's a really sweet dog but I completely understand your fear, because he's huge. When you feel frightened you can come sit here with me". And then just be matter-of-fact about it, and don't try to make her interact with the dog, or make her drop her caution.