Fortunately, WoW sport developer Jeremy Feasel affirmed the zombie invasion part of the event will only be active for a couple of hours throughout the day instead of all the time. I'm actually a bit disappointed with that, honestly, because I believe it would be fun to find yet another all-out, 24/7 invasion which gamers need to try and contain--something similar to World of Warcraft's notorious Corrupted Blood incident.
Players may also venture to the frigid wastes of Northrend to fight bosses and make strong loot, and there is also a new story quest to test out.
Otherwise, you can wait until the event inevitably starts sometime in the forthcoming months. But now that it is on the PTR, it'll likely be occurring sooner rather than later