Not a bad result.
In fact, you seem to have a good understanding for the problem. There isn't much you can do except to get a faster lens such as a constant F/2.8, then your shutter speed would be 1/1000 (at F/2.8) instead of F/5.6.
A flash would give you better result assuming it's not out of reach.
Or you can set to higer ISO. That will give you sharper shot but more grainy images.
Nikon D90, D80
Nikkor 16-85mm AF-S DX F/3.5-5.6G ED VR, Tamron SP AF 28-75mm F/2.8 XR Di LD Aspherical (IF) macro, Nikkor 50mm F/1.4D, Nikkor 50mm F/1.8D, Nikkor AF-S VR 70-300mm F/4.5-5.6G IF-ED, Sigma 105mm F/2.8 EX DG Macro ||| 2x SB800 | SB600 ||| Manfrotto 190XB