Although the FAA is of course involved, it's generally the NTSB that is the lead investigator in airplane crashes. The NTSB already has jurisdiction to investigate highway accidents.

There's also NHTSA (which is indeed part of the DoT).

It looks to me like we don't need any new agency at all, just a very small expansion of NHTSA's mandate to specifically address the "self-driving" part of self-driving cars.