To move your library to a new computer all you have to do is copy the library database over. To do this, copy the folder located (in your home folder) at ~/Library/Application Support/Delicious Library/ to the same location on the new computer.
You may also wish to move over your settings and license code. To do this, copy over the preferences file, which is located (in your home folder) at ~/Library/Preferences/com.delicious-monster.library.plist.