If you only have a W-2 and a 1099-DIV, then NO, you do not need premier for those two items. I can't speak for any other tax situations you may have, but the Free Edition handles both W-2 income (under Wages and Income) and 1099-DIV income. (under Interest and Dividends)
If you
have 1099-MISC, you will have to upgrade, but not for 1099-DIV.