If the permanent is already untapped, you can’t activate its {Q} ability. That’s because you can’t pay the “Untap this permanent” cost.

When you activate an {Q} ability, you untap the creature with that ability as a cost. The untap can’t be responded to. (The actual ability can be responded to, of course.)

If a creature with an {Q} ability hasn’t been under your control since your most recent turn began, you can’t activate that ability, unless the creature has haste.