I can def see where a 'Quick Print' option which I use "All The Time" at work (particularly in MS Office) would be really nice for a lot of users.
All I can say about having to drag a file to an icon on the desktop as advised here would be a pita...
I'm looking at a multi-page spreadsheet I just created from one of our default blank workbooks I use all day long, looking at a single page of that workbook where I can click the 'Quick Print' icon and send it direct to the printer.
This option of needing to find a document in Finder - or modifying the window size of the app you're working in and have to drag that to an icon on the desktop, would quite frankly suck compared to having the dialog open which means you just end up clicking on 'Print' twice.
The best answer to me is, No, there is no way to accomplish what you want that makes it easier than clicking on 'Print' twice instead of once.
I can definitely click twice in a shorter period of time than grabbing, dragging and dropping something.
It's not "always" greener on the other side...