Drone carrying a video camera

Drone equipped vehicles passing other drone equip vehicles (going in either direction) just might be a problem.

EDIT And then there are cloverleafs with under and overcrossings.

You are gonna need a long wire. Battery life on most drones is measured in minutes, and forward flight with control is difficult from a moving vehicle.

A couple of thoughts on your idea, while interesting it presents some legal challenges. The FAA very recently clarified the rules to ensure that Drones are part of the RC Model Aircraft rules, which have one important gotcha... for it to be legal you must be able to maintain eye contact at all times. This rules out any kind of Autonomous Drone or drone being piloted by Oculus Rift VR goggles (which I have seen done and is very cool). The other thing is most drones tend to have a kill switch so if you go out of transmission range it simply falls from the sky, the can get expensive if you loose contact too many times. To rain on your parade even further, the US Park Service has made them illegal to fly at any national park/monument.
However if you want to come visit Canada, we are quite behind the times on the legal requirements of Drones, so you can do any of these things up here... for now.
BTW if you are looking for a drone with a camera, DJI Phantom right now seem to be the benchmark for pre assembled drones, but they are pricy.

Unfortunately, some people are ruining it for the rest. They are starting to restrict the drones more and more now. There are already many state and municipality laws concerning them and the FAA is trying to get their hand in on them as well. Lately being that if you are using one for commercial reasons, then you have to have a pilots license. This is of course if you remain legal.

mrjmrobertson wrote:
Here's one that will follow you around...

https://www.lily.camera/

Liliy is really cool. But it's only setup to follow people around, not vehicles at speed.

Here's one that will follow you around...

https://www.lily.camera/

Of course, the drones with cameras exist and are even affordable priced. Here's one example for less than $200. It would also be nice to be able to record what is seen.
http://www.amazon.com/gp/product/B00M2G1UVI/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=B00M2G1UVI&linkCode=as2&tag=flyingdronese-20&linkId=AEHJCXWO7HYWDDAX

Only if it is linked to a monitor that is not visible to the drivers line of sight.