I'd also make sure you give JJ a chance to clear her beak a bit.  Maybe give her water in a small bowl once a day so she can dip her whole beak in.  I know ducks like to do that sneezy thing into water.
She should be old enough soon to enjoy a small bath, in that case, the bath should help with watering her beak.
I used a small pet waterer like yours but found after a week and a half to two weeks later, it wasn't enough water for them.  I then used a mug after that.