Bag the car. I have worked in Peru as an exploration geologist for years and drive quite a bit in country. However, there are places that as a gringo you just don't want to be and you can't really know those places without a good knowledge of the country. Also, you would not want to try this unless you spoke VERY GOOD Spanish - and up country much of the Spanish is mixed with Quechua. You will find that no one will speak English outside of the touristy areas.

Driving would add considerable time and aggravation to the trip. Roads in the high country follow contours of the topography and take much longer to cover any distance than one would expect. They are also rather narrow and often marginally maintained. If you do want to rent and get off the beaten path, you can rent locally in most larger towns - Arequipa, etc. Rent-Andina is probably the best choice for cars/trucks outside of Lima (www.andinarentacar.com.ar).