Yes, you need enough SQL Enterprise licenses to cover all 16 cores, however one SQL Enterprise license = 2 cores. So for a 16-core server you'll need a total of 8 licenses.

To add to that, each license allows for an offline mirror. Meaning you can setup database mirroring, or an unreadable AlwaysOn secondary in a DR site if you want. However, if you want an online mirror, as in a readable secondary for Read-Only Routing, you'll need full licenses for the secondary server too.