Puritan belief system. One of the tenets of Puritanism is that Satan can and does appear in physical form in order to tempt the righteous into sin. After all, the 1692 witch hysteria in Salem, Massachusetts, which culminated in the execution of nineteen women and one man in 1693, was based largely on what is called "spectral evidence"—that is, the theory spirits of living people who have become witches can cause harm to other villagers and livestock while their physical bodies go about their normal life. More importantly, Puritans also believe that Satan can attack them in dreams while they are sleeping, because their religious defenses are weakened during sleep.

When Faith implores Goodman Brown to postpone his walk in the forest until daylight, she is responding to two fears. First, as any villager in seventeenth-century Massachusetts would know, the forest is a very dangerous place, especially at night, because of Indians. Many villages, even through the eighteenth century, were palisaded against potential Indian attacks, and attacks on Puritan settlements occurred on a regular basis. Faith's plea is partially based on her fear that Goodman Brown will become a victim of violence. Second, she understands her own jeopardy if left alone:

pr'ythee, put off your journey until sunrise, and sleep in your own bed to-night. A lone woman is troubled with such dreams and such thoughts, that she's afeard of herself, sometimes. Pray, tarry with me this night, dear husband, of all nights in the year!

Faith is articulating her dread of being left alone at night because she knows she is susceptible to an attack by Satan in the form of a dream that could turn her away from her Puritan belief system. Her danger may also be enhanced because, as she alludes to "of all nights in the year," this night might be All Hallow's Eve, a night when Satan has additional power to tempt a young Puritan woman who is alone.

Hawthorne never directly says that Faith knows anything.  He intentionally leaves it ambiguous, but he does mention at the beginning that Faith is afraid she will have bad dreams.  After she mentions this though, Young Goodman Brown says he sees a troubled look in her face and wonders if she's had dreams that warn her of what will happen that night.  

In addition, you have to consider the Puritan setting of the story.  Puritans believed that the forest was the place of witches, heathen Indians, and the Devil.  They also believed that nighttime harbored evil deeds.  So for Goodman Brown to insist on traveling into the forest "twixt now and sunrise" would automatically make a good Puritan, likeFaith, afraid.  Goodman Brown also states that "of all the nights of the year, this one night must" he leave her.  This statement makes the reader wonder what night this is...it could be a specified time of year, such as Halloween, that might add to Faith's anxiety about his journey.