I'm a huge fan of a label with some basic care information.
People don't plan on having an accident when they get in their car. People don't plan on becoming unable to share information in the event of an accident.
Depending on where you are it can take a while for someone to claim an animal left at an accident scene, either family or animal control.
One note about the carrier being removed, if it isn't in the way of getting people out, it will leave after people are removed. If there is a major hazard like a fire or explosion risk and you have to be taken out by emergency personnel, there is a large possibility your animal will not be removed. Yes, this may seem obvious but it's shocking the things people will complain about towards emergency responders at an accident scene.