Definitely sounds do-able and a lot of fun to boot. A well-tuned PID loop should keep things smooth. Outdoors, a sub $20 GPS module will track speed to better than 0.1m/s. It wouldn't be accurate enough for position within a running lane, but combine it with an OpenCV model for lane finding (eg: ) and you'd have some useful data to choose from, as well as maybe a "return to base" feature.

TBH - knock your socks off and let us know how you go.