Both sound a little strange (US English) without some object. My daughter is studying at State College this Fall. My daughter is going to study at State College this Fall. Both are fine ways to say something is happening in the future, though.

Both are good the way you wrote them. Use them the same way you would in Spanish. :=) Mi hija estudia este Diciembre. My daughter is studying this December. Mi hija va a estudiar este Diciembre. My daughter is going to study this December.