The two upgrades which make the biggest difference are the wheels and the frame itself. (I know, better shifting is fun but it won't change your speed/distance much) You could also look at getting better tires, but since you have a commuting bike they should already be fine.
Given the price of a good wheel set you might be better off with a complete bike. Now the type of bike really depends on the road you're cycling on. You mention commuting, if the majority of your time is spent riding in the city you'll enjoy a higher-end commuter more than a race bike.
Also, since you started cycling quite recently, you'll probably get faster with time as your "bike muscles" and your cardio get better. I don't know how fit you were to begin with or how frequently you've ridden your bike in the last 6 months, though.