Yes, it is suggested to transplant your herb plant every couple months to encourage more root growth. It is simple to repot your plant: choose your new, pot, fill it with potting soil, and plant! Be sure to loosen the root ball before planting. This allows the roots to breathe more while adjusting to their new pot.
Here is some info on harvesting your herbs: harvest your plant by 1/3 at a time and no more. This will allow the plant to create more leaves and will not stress the plant. Harvesting all leave off at once may kill the plant and it may be difficult for them to recover. If they still have leaves on their plant I would recommend transplanting to see if it comes back.