Depends whether you mean Cydonia flowering quince or Chaenomeles flowering quince - the first becomes a 20 foot tree, the second is more of a shrub with bright orange or red flowers on bare wood early in the year, followed by leaves. The second can be hard pruned, and will be easier to move as its a shrub, although after 4 years, it'll likely have a large and good root system. Best time to move it would be autumn or winter. If its Cydonia, 4 years means less success in moving it at all, as it tends to put down tree like roots.