I'm at the point where I can fight and beat Elder Scrolls V: Skyrim but I don't really want to finish the game yet
Yes, it is possible to learn Dragonrend without beating Alduin. However you do have to finish a majority of the main quest.
Dragonrend is learned during the Alduin's Bane quest, where you travel temporarily back in time to see how Alduin was captured the first time around. Once you've completed this quest, there's only four more story quests to finish before you're done.
In addition to Mage Xy's excellent answer, please note that killing Alduin does not "finish the game". Skyrim is completely open world and it really doesn't distinguish the main quest line from any of the others. I've done play-throughs where I finished that quest-line first, then finished the rest, and others where I've never even started it (which is nice because you don't get constantly attacked by dragons). So, don't be afraid to finish it... and in your next play through try not starting it at all and enjoy a sky free of dragons.