We had a guy ride a track day on a dual sport dirtbike (he was durn good on it too).
I've had this talk with a few guys I know. I suggest an SV650 that's already track-prepped (racing plastics, no lights/signals, etc). Thing is that they are in high demand, which drives the price up a lil bit. A good choice for about the same amount though would be an older Honda CBR 600 F2/F3 . While they're not super cutting edge best everything you can buy today, they'll still be faster/better handling than what 99.9% of the general population can handle anyways! And finding a track-ready bike isn't too difficult. Just check the WERA classified's and such.