The DPI setting coming out of the camera doesn't mean much (if anything). You have a fixed number of pixels coming out of the camera (4272 x 2848, to be exact). Since you're enlarging it quite a bit, you probably want to shoot in raw format to ensure you get everything that camera can produce.

Once you've done that, you might want to "upres" the picture to fit what the printer has asked for. In this case, that'll be a resolution of 10800x7200 pixels, which means more than doubling the resolution in each dimension.

There are several ways to do that. There are some programs written specifically for that kind of task (e.g., Perfect Resize). You can also do this in Photoshop using `Image -> Image Size". There are tricks you might try using in Photoshop to see if they improve your results (but do look around -- different methods work better for different subject matter).

Once you're done, the picture shouldn't look drastically different on screen, though when/if you zoom in to 100% at the increased resolution, you can expect that it won't look particularly sharp -- a bit better than if you just zoom in to 250-300% on screen, but (honestly) not a whole lot. At the same time, it's a fair guess that people will generally be looking at a 48x108 banner from a fair distance away, not up nearly as close as most of us look at our monitors.

Given this level of enlargement, however, you do want to be as careful as possible to ensure the picture is sharp -- you probably do want to use either flash or a tripod (or both), especially shooting indoors (where the light is usually relatively dim). You probably also want to set your aperture to about 2 stops below the maximum for the lens to get the best performance it can provide.

If your subject is something that stays perfectly still, you could also consider shooting a number of overlapping pictures of parts of the subject, and stitching the pictures together. Photoshop can do this, and there are also tools specifically for the job such as Hugin and Microsoft ICE. These can give you a picture close to (or even greater than) the overall target resolution (but as I said above, this probably isn't a major problem).