The bad news: you need a DCC command station. Computers output serial information (in one form or another). The component that puts DCC on the rails (the booster, usually incorporated in a command station) needs something to take that serial information and make it into DCC commands (specific voltage levels on a wire, not "serial data" in the sense that a computer thinks of it) that the booster can then amplify.
The good news: there's actually a small box that combines USB adapter with command station and a very small booster (suitable for several N-scale trains of modern design). I've never used one, but it sounds like it would meet your requirements. It's called a
SPROG.
I use a Zephyr, Locobuffer USB (similar to the PR3, see
this page for a comparision of the two) and JMRI. That gives me some additional options (transponding support for train to command station signaling; ability to control accessories via loconet, separate from the track; ability to add boosters for more track power; hand-held walk-around throttles). But for a small layout, if you don't want fancy automated control (the main use for transponding), then a computer + SPROG combination should be fine.
This, by the way, is my 1,000th post on the forum. Woot!