Do I declare the 550.92 amount shown in a1 and a4 on a 1099 DIV when this qualified dividend is automatically roll in toward the purchase of more stock?

[SusanY1]

Yes, even when dividends are reinvested you will include them in your current year income.  This amount will also increase your "basis" in the stock (or other investment) which will lower your capital gains when you sell the investment. 

Unless the dividends are in a tax-deferred account such as an IRA, they will always be taxed in the year in which they are credited to your account.  

Qualified dividends are taxed at the same rate as long term capital gains - so depending on your overall income there may or may not be any actual tax due on the reported dividend income. 

You can learn more about how dividends are taxed HERE.