Use google earth to determine the square footage of the roadway you want to pave. Find an online asphalt calculator to tell you how many tons of asphalt it will take, use 3" for depth. Once you get an idea of tonnage, find out the cost of asphalt in your area and that will give you a estimate of what the material cost will be. In NE Ohio, asphalt is running about $80/ton. Depending on the contractor, it will cost anywhere from 2.5 to 4 times the price of the asphalt to put it down. All of that is assuming the the current gravel road does not need any repairs or preparation prior to putting down the new asphalt.
A couple of things: look for where the water runs off, nothing destroys a road faster than poor drainage. Fix any drainage problems or you will be throwing your money away. Also, overtime, roads have a tendency to get wider, especially at intersections. We are working on the roads in our park and some of the intersections have grown over the years into literally boulevard size status, we are to grade those back to what they were, one upside is it will take less asphalt to cover. But JD is right, nothing beats an actual estimate.