It won't really be that complicated. If you earn any dividends between now and the end of the year, your brokerage will send you a statement telling you how much you earned. You report that income on your taxes as Dividend Income. That's it. Pretty simple.
And unless you are sitting on a shit ton of cash to invest, your dividend amount is going to be pretty meaningless to your taxes. For example, while I'm not invested in dividend specific stocks, I do receive dividends as part of holding index funds. My $80k account returned less than $1K worth of dividend income for the whole year.
I'm guessing you have less to invest than this, and you're only investing for a month, so I see no reason not to get started now.
(also, my index funds pay out quarterly but on 1/31, 4/30, 7/31, & 10/31 for whatever reason, so I'm done earning dividends for the calendar year already. If you're still concerned, look up the dividend schedule on what you want to invest in, as you could easily invest starting today and not see a dividend until 2014.)