You need to analyze your "feelings" as to why a P&S isn't doing it for you and come up with concrete reasons that translate to camera features. If your general thinking is just that your pictures aren't pretty enough, then you're right to hesitate and do some more research. Cameras are simply tools. Taking the picture is still up to you, and in the right hands, P&S cameras can actually be used to create stunning pictures, within limitations. If you simply google for images taken with the same camera you have, you'll undoubtedly find that the camera itself may not be as limiting as you think it is.
The difference between a snapshot and a photo is not the camera it's taken with--it's the amount of thinking time, vision, planning, and effort that went into taking it.
However. If your frustrations with the P&S camera are specific and concrete, and those translate to camera features you can only get with a dSLR, then maybe it's worth the expense and time. But these days, many of the old reasons for moving to dSLR may no longer require a dSLR.
If all you want is thin DoF (blurry background), then you may simply need a camera with a larger sensor and a faster lens. There are fixed-lens cameras with dSLR-sized sensors in them these days, and every size in between. There are also interchangeable-lens mirrorless cameras that can achieve the same thin DoF, and even P&S cameras with small sensors can achieve this at macro subject distances.
If you simply want more control over exposure settings, and your current camera lacks the "PSAM" (i.e., Programmable auto, Shutter priority, Aperture priority, and full Manual) modes, then all you need is a camera that has those modes on the dial; a lot of fixed-lens "enthusiast" P&S cameras do. If you want more control over post-processing, then you may simply need a camera with RAW capability (or, if your camera's a Canon Powershot, the CHDK). If you want more control over lighting, then all you need is a camera with a flash hotshoe.
None of these things requires a dSLR, although a dSLR can certainly deliver these features, too.
To my mind subjects that require a dSLR (and even this is changing) are those where you need super-fast responsiveness. Where you have to time the shot exactly. Where you need the autofocus to be super-snappy to follow a moving subject. Or, subjects that require more exotic gear (say, tilt-shift lenses) that can only be found in dSLR systems at this time.
Renting or borrowing a dSLR and a lens and shooting with them is probably the easiest way to find out if this is for you with minimal outlay. You may be surprised at how large and unwieldy the gear is or how limited a single lens may be, compared to, say, a bridge camera (i.e., no macro modes or supertelephoto reach without dedicated lenses).