Your first sentence is not quite right. I think "She quietly fell into a dream on the beautiful night." would sound better, or you can still say "Quietly she fell into a dream on a beautiful night. Your second sentence is perfect. Other examples along these lines would be: The cat walked quietly up the street. I carefully stacked the plates. A puppy was playfully chasing it's mother. Hungrily, the little girl took the cookie. I used to speak Spanish so easily.