Carry your passport. But keep it safe under your clothes in a special pouch.
When you need to proof your age try your driving license, if it is not accepted you can pull out your passport.
If you have a passportcard you could try that, might still not work.
A paper copy of your passport is very unlikely to be accepted, too easy to fake or change details.
As per Mexico City's airport website, foreigners are required to present their passports when traveling on domestic flights, so the answer is no - you will not be allowed to board with just your driving license.