Welcome to the forum!
Yes. The "G" lenses will work on the D7000. I am no expert, but a G lens is a G lens. The zoom range of that lens may not satisfy you at the low end, due to the "crop factor," but the lens is usable. If you find yourself having to step away from your subject more than is convenient, in order to compose the image, you may want a wider-angle lens.
Canon 7D/5D/40D/1D2N; Nikon F6, D700, FM3A, & Coolpix A; Canon 40mm 2.8 STM, 135L, 50L, 35L, pre-II 50mm 1.8, 100mm 2.8L Macro, 10-22mm EF-S, 28-135 EF, 400mm 5.6L; Nikkor 50mm 1.2 AI-S, 50mm 1.4G, 50mm 1.8D, 16mm 2.8D Fisheye, 180mm 2.8D, 100-300mm 5.6 AI-S; Tokina 17mm & 100mm 2.8 Macro