Ok, I hate to break into the gear-fest party, but you do need to ask yourself some very solid "Is it my gear, or is it my technique?" questions before starting to open your wallet and begin the neverending quest for better glass. Particularly if you're after something sharper.
Question 0: Do you know
how to hold your camera?
Question 1: Are you sure it isn't a focus/depth of field issue? If you recently made the jump from a P&S camera to a dSLR, you're not used to a camera giving you a DoF and the possibility of something being out of focus. Check the other sections of the photo to see if something else was in sharp focus. The autofocus system of your camera is dumber than you. It may not have targed the right object in the image. Learn about stopping down to increase the depth of field and about mastering your autofocus system.
Question 2: Are you sure it isn't motion blur? Particularly in low light, you may find yourself with shutter speed issues. Doubly so if you answered "No" to Question 0. Stablization can only help you so far. Learn about tripods. And about the 1/focal_length rule for longer lenses.
Question 3: Are you shooting wide open? Or at the focal length ends of the zoom range? No lens is at its best at its maximum aperture. Using an aperture that's one or two stops down from your max. will help your lens perform better in terms of sharpness, CA, and vignetting. f/8 is a typical sweet spot for a lot of lenses. Also, with zoom lenses, they tend not be at their best at the extreme ends of the zoom range. Change it up a little, and see if that helps you eke out some more performance.
Question 4: Did you post-process? Learning simple post-processing like sharpening and curves adjustment can work wonders. A P&S camera probably was automatically applying sharpening and saturation to your photos. But a dSLR by default typically doesn't--it assumes you want to flavor to taste based on the individual image. Learn to polish up your photos on the computer.
If none of these techniques helps you,
then it's time to start looking for a new lens. Because if you haven't fixed these four basic issues, a new lens might just disappoint you. To get the best out of a "better" lens, you need to master basic technique first.