The quest giver Handyman is funny.... it seems, he hands out the quest in a willy-nilly basis.
I have both good/bad toons, level 53, 53 above toons, you name it.
I have loged the quest with some and not the others. There seems to be no set rules to whom may do it or not!
Good luck getting the quest, in my opinon, the quest aint worth it, compared to an "other" hunt-n-gather quest. The distance to Ratmen, all the possible ADDs, even ADDs of casters. However, if you are going to farm there, you may as well do the quest too.