The only difference for you for dirt will be engine and tires.
Engine 25 races, top end rebuild, 25 more. Now the debate begins, some say full rebuild and repeat. Others trade the core in ($800) and buy a new one. Supposedly rebuilt motors cant hang with motors on their first cycle. This is asphalt were power is more important than dirt.
Tires $550 x 3, the more you cut the tires, they will be faster. A set of tires cut to last 1 race will be almost 2 tenths faster than tires cut to last 3 weeks. Welcome to the land of the rich daddy's who's kid is destine to be the next Jeff Gordon.
Talk to Dennis Lambert, Ryan Farbo, or Devo for tires.
By the way they do run dirt at Rockfish and Fayetteville, but that's near the coast.