However, they do not actually travel to the Q home planet in this episode. Instead, Q brings the Enterprise-D to a "random point" within the Q Continuum. This point resembles a vast expanse of emptiness with an enormous structure in the distance, which is seemingly the Q's home planet. However, this is never explicitly confirmed.
The episode does suggest that Q has a home planet, and that there is a "Q Continuum" where they reside, but it does not reveal the name or location of this planet.