Hi,
Short answer: it will fit, but it won't autofocus. And optically it sucks. You'll need lenses with AF-S designation.
Longer answer:
there are two versions of 70-300G. The older is
AF 70-300 f/4~5.6 G and the newer
AF-S VR 70-300 f/4.5~5.6 G
The former lens doesn't have its own focusing motor, so it requires that the camera body has a focusing motor. Your camera doesn't. The latter lens fits and focuses in your camera, but is a lot more expensive. In the current camera lineup the "lowest" bodies with focusing motor are D7x00 and D6x0.
How about AF-S VR 55-200mm f/4~5.6G? It is optically good, has camera shake reduction (VR), is reasonably priced and will autofocus with your camera body.
Sidenote: There's also a third 70-300, but that won't autofocus with your camera either, although optically it is pretty good: AF 70-300 f/4-5.6 D ED. I won't recommend that either for cameras that don't have the autofocus motor, but otherwise it is a good walkaround performer.