My daughter is a full time student . She was twenty years old by end of last year.She worked for a company last year part time and they have sent her a 1099-MISC for about $6000.00. Is she considered a self employed person?Their employer calls her a consultant, apparently. I am claiming her as a dependent. Doe she have to file a tax return?

Yes this is considered self employment income, there was no tax paid out of this, normally she should have been paying estimated quarterly taxes including self employment taxes ( social security)

Thanks for your answer. What forms would she have to use?

How you will report the 1099-Misc income on your tax return, read:
Your U.S. Tax Return: W2 or 1099: Employee or Independent Contractor. (http://taxipay.blogspot.com/2008/03/w2-or-1099-employee-or-independent.html)