I'm sorry for those who haven't been able to get the comic yet, but this is fantastic! How often do comics go to a second printing? Everyone involved in making this title happen should be proud.
Less often than you think. Comics these days are printed to order for the most part, that means that the distributors (and there's really only ONE major comic distributor, Diamond) collect pre-orders from all their consituent comic stores, and then the comics companies pretty much print to fill that order, with usually a 10 to 20% overprint to cover. That being said, it's completely different between the big companies (Marvel, DC, Dark Horse and Image) to the smaller publishers (like Dabel). Smaller publishers have a lot more on the line than bigger publishers, so smaller press runs are the norm. We know that Dresden Files #1 was printed at over 10K copies, but we haven't been able to nail down an official number (Diamond's sales numbers will be out in a month or two for this month).
Still it shouldn't be too difficult to go back to press, as long as the printer has all the galleys and such. Unless they decide to change the cover (which IS common on a second printing), in that case it might take a little while longer.
I would venture to guess that the second printing of #1 will be timed to release with #2 for those who missed it. I could be wrong though, however synchronicity is an important thing in retail.