Is this a good chapter one so far?

I think it was a bit rushed and yes you do need to start a new paragraph every time a new character speaks. In the beginning instead of just saying that she awake with a start and saying how she had a bad dream, describe the dream as the beginning instead of just saying gosh that nightmare was horrible. Also when she walks outside is cold? Is it warm? What does it look like. Try describing most things and your chapter will be very good. Also, with the name of the chapter it makes no sense because it ends by the little girl talking. The readers expect for Alicia Reynolds to be murdered. Or killed. So just saying that the name is a little off.