While most quests are indeed not repeatable, you can indeed accept them on any class you want, do them on another class and then switch to a third one to turn them in. The only requirement for most quests is that your level is high enough to accept them and turn them in. (Back when I started the game I could accept some level 50 classes because my culinarien was already level 50 while my paladin was only 34) Specially between DoW/DoM thats not an issue! You can accept and do quests on your WHM now but hold off on turning them in until your archer needs exp and has a high enough level to recive the rewards for them!

Beasettribe-quests are repetable - but at least the HW and SB ones lock you into the job you're currently on. So: If you accept those quests as WHM, you can only turn them in as WHM.