She'll be right shoo. From experience I've wrote four thousand, or close too, in one night.
It won't be hard. When you think about, 6000 isn't alot. You still have more than a term. There are ten weeks in this term. Divide 600 by ten, you get six hundred.
Divide six hundred by seven and you get a little over eighty words a day (I could waste time working it out exactly in my head but it would be far easier for you to get a calcutor).
Eighty words a day is maybe one minute of crap writing, and five minutes or so of thorough, decent writing....
Think of it that way.