paint programs printing

I have been messing around with various painting experiments in QC and now I have come to a road block that will basically make any paint program I finally develop useless to any anyone that wants to create high rez printouts. On the mac the screen rez is 72 dpi. On my tower I am running a HD 1080i output to the monitor which looks awesome on the screen. I do a screen capture and as soon as I print out anything bigger then a post card the resolution is not high enough and the print out looks fuzzy.

300-600 dpi is an average printer. I think to get a decent large print I would need to do a screen capture with a screen that is 3200 by 1800 minimum and 6400 by 3200 would be best.

So the question is is there a way to fake it how can I make a high res print from a QC program with out having to render it to my monitor,

Or any other solution for this problem would be welcome as well