As you said, you'd never leave dog and baby unattended. So the dog would not have the chance to "run all over" the baby. But if the dog accidentally did, she would probably cry which would make the dog realize...Ooops! Guess I shouldn't do that again. Just as if another dog yelps.
Not that I want you to LET the dog hurt your daughter.

And Karen is right, the baby (and the dog) feel your tension. I know this, but I have not learned how to not feel tensed myself. I have a different issue with my dog and me being stressed and sending that stress to her. So, if you figure out how to supress the tense feeling, please, let me know!

Good luck!