Do I need to complete specific quests on an alt to access a WQ?

I'm working towards all the quest achievements for TWW currently, and there are some achievements that require a world quest unlocking, e.g. the achievement 'Never Enough' requires you to do 'Pool Cleaner' WQ which is unlocked after doing 'An Orphan's Request' quest.

If I have already completed An Orphan's Request on my main - do I still need to do that quest on an alt to unlock the WQ? Or is the WQ unlocked by default since i've already done it on my main?

Thanks