Pretty much it. I pvp only on my Hunter.
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As much as it sucks, if you want to do that quest as is, then you're going to be punching and grenading your way through it. If you want it on your hunter, you'll just have to hope RNG gives you the same quest on your Hunter. I don't know if it's a One-per-account quest or not, but I do know that all quests are character specific and can't be transferred once received.
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I don't think so man. Just grind it out