Yes, a pooja is necessary before shifting in into government quarters. The main reason for puja is to drive out the negative forces in the place and install positive energy in the place. You might not be aware what kind of things might have happened in the place before your arrival.
So it is always safe to conduct a small puja to drive out all the negative energy and install positive forces in nature.
The best option is to perform Ganpati puja or Shiva pooja.
A puja always benefits the doer in numerous ways.