Perhaps you may be afraid deep down that your little girl is sensing something that no-one else is aware of?
Yet you have said your brother's dog is a very kind sweet character. It would be rare indeed if a generally sweet natured dog suddenly turned. It can happen, but it's rare, and would be likely to be caused by something like protecting pups, or food guarding issues, or an illness, or mental deterioration such as dementia etc.
But her fear could have a few origins maybe.
Your Border Collie is 'hers', a well known family member, probably almost like a sibling by now. They are familiar with each other. A Border Collie is also smaller than a mastiff, and looks very different facially.
Mastiffs are wonderful handsome dogs, but some can look a little 'scary' in the facial build, even if they are sweet natured.
Your brother's dog is not a close member of her family. You may think so, but to a little child she is more used to the tight-knit group at your own home. Her trusted closest family members.
Has she ever seen -in life, or even on videos or movies -a similar-looking dog to your brother's Mastiff, involved in any scary scenes? Or even involving barking threateningly in any scene? (that might be hard to remember, but a very young child could remember because it may make a strong impression on a young child.)
Maybe it's the kind of bark your brother's dog has? Deeper and louder and more imperious than a Border Collie?
Cast your mind back to the very first meeting your daughter had with your brother's dog. Was she jostled, even in a loving friendly way by the dog, perhaps as a greeting? If so that might have caught her at a sensitive moment, especially if there was barking at the same time. How much bigger is the dog than she is? That might be intimidating for her.
And can you remember if you yourself, were a little intimidated at all, but over-rode that when you saw what a nice dog she was? Your daughter could even have picked up on that cue if you did. Children can be very sharp and intuitive. (I am not saying that happened, just exploring all possibilities.)
Or if she first showed a bit of nervousness in those first few moments, did you pick her up very quickly, perhaps before she had properly greeted the dog or drawn her own instinctive conclusions? That would definitely have sent her a sign that was a protective move from you. (again, not saying you did, just exploring again.)
And lastly, for some unknown reason, we can form likes and dislikes sometimes to anybody, any character, any dog or animal, as they can for humans. We can fall in love for no apparent reason, and we can 'just not like someone' for no apparent reason. Sometimes it happens.