Little dog chasing big dog?

We're out all day tomorrow so my 11 week old female puppy is going to a friends she has a very quiet dog alot bigger that mine (dont know the breed but its got alot of wrinkles very wrinkly dog) its a female. And we took my dog around and i thought shed be scared but she ran after my friends dog chasing her. my friends dog ran upstairs she was that scared. isit possible that tomorrow when my puppy goes round for the day that the dog might get wound up and rebound back or anything. the owner is going to keep a good eye on them both. will everything be ok? thanks. Isit common for a big dog to be small of a small dog? thanks