Quakers, like most parrots, have "major" and "minor" molts several times a year. The major molts, in which they lose maybe a third of their feathers, are usually noticeable and most often occur in late spring and late fall. The minor molts you will probably not notice except for clipped wing feathers growing in, which is a good reason for checking the wings every couple of weeks.

In the wild, a parrot that is not able to fly well is a dead parrot, so they molt matched sets of feathers at different times, thus always retaining the ability to fly. For example, if you see the 2nd and 5th primaries coming in on the left wing, the same two will also be emerging on the right wing. Molts can be delayed or brought on by malnutrition, good nutrition after a period of malnutrition, breeding, stress, moving, and major weather or temperature changes.

Pinfeathers are new feathers growing in. A significant amount of pinfeathers generally indicates a molt, but feathers will regrow immediately (well, in a week or two) if pulled out. Smaller contour and "down" feathers are constantly being lost and you may see a dozen of these small feathers in a week, but you shouldn't see more than 1 or 2 larger feathers in a day from natural losses.