Downie will remember your previous downloads (unless you turn this off in Preferences > History). To access the history, select Window > Show History in the menu bar or click on the History button in the main window. The history in the current version is a very simple list of previous downloads with the arrow button that will select the downloaded file in Finder. When you right-click a row, you get an option to open the original link the file was downloaded from in your browser.