Is there some way to quickly print a single copy of a file without having to go through a Print dialogue box?
Yes, if you do it in the Finder. Just open System Preferences, choose the Print & Scan (Lion) or Print & Fax (Snow Leopard) preference, select your default printer and drag it to the desktop. Do this and an alias of your printer appears on the desktop (termed a desktop printer).
When you want to print a quick copy, just drag a file (or more, if you like) on top of the desktop printer and, in short order, your printer gives birth to a printed copy of your document without an intervening print dialogue box.
Regrettably, there’s no system-wide command for quickly printing one copy of a document from within an application. A few applications support such a thing – Microsoft Office applications, for example – but as printing is increasingly an “old-school” activity, I wouldn’t hold my breath waiting for other applications to implement such a feature.