Does my daughter have to pay taxes on a 529 plan if the whole amount was paid to her college for tuition room and board plus meal plan ?

no

as long as the qualified expenses exceed the 529 distribution, there is no tax on Box 2; in fact there is no need to report the 1099Q on your taxes in any event

However, it may be worth looking at the total picture to ensure you are taking advantage of AOTC.  The tax credits there are worth a lot more than what may be a small amount of tax to be paid by your dependent; and her income may be so low there is no tax to be paid at all? 

if you answer these questions I can suggest if there is a  better path:

1) Box 1 and Box 5 Form 1098T

2) Box 1 and Box 2 Form 1099Q

3) any expenses (think room and, books and computer costs not included in Box 1 of Form 1098T)

4) are you eligible for AOTC?  Is your income below $160,000?

  5)  whose social security number is on the Form 1099Q? yours or your daughters?