The DRZ is a great bike, and it's really not too tall for you, but you just don't know it yet due to inexperience. Either learn to ride on something else, or get a set of lowering links from Norm Kouba.
http://www.koubalink.com/
Set your sag according to his instructions and slide the fork tubes up an inch. You will probably need a shorter side stand.
Once you have some experience on the bike, you may want to return it to stock height.