I have the same disatance, all flat. On my road bike it takes from 35 to 50 minutes depending on traffic lights, wind and myself. Normally, it is about 45 minutes.
I would not buy a road bike, unless you are just looking for an excuse. I'd change your seat post first, if it is not rigid, then the front fork to a rigid one. Tires high pressure 1" Continental Gator Skins slicks.