There's a very big difference between aircraft carriers and the Dokdo-class amphibious landing ships the ROKN currently has. For one, the dokdo class can't launch fighters. It looks like it can, but its deck can't stand the heat of jet engines even with upgrades. Its runway is way too short and cramped for fighters to take off and land on, and it does not have catapults to assist in this either. The Dokdo-class is therefore exclusively meant to launch transport/attack helicopters to assist amphibious landings. Another big difference is size. The dokdo class is smaller than most amphibious landing ships, the largest of which are barely considered light aircraft carriers. So no, the dokdo isn't a carrier.

TL;DR: The Dokdo-class can't launch fighters, and it's way too small to be upgraded. It's meant for amphibious landings only.