Yes, Q=CV equation is somewhat misleading in this context. A capacitor doesn't store electrical charge, it stores energy. This is a very common misconception, when we say 'charge a capacitor' we don't mean put electrical charge into it, we mean put energy into it. The plates are equal and opposite in electrical charge due to an abundance of electrons on one plate and an equal and opposite charge on the other. The total stored electrical charge in a capacitor is zero, and the Q=CV equation relates to how much charge flowed *in and out* of the capacitor (in fact since electrons can't cross the barrier between the plates, it actually describes the *modulus* of the abundance of charge on each plate, one abundance is positive and the other is negative).
Mark.