if you already have a moon you can't have second one on same plant.
so build extra ship would be useless if want another moon.
and the best ship for moon-shot mission is battleship or light fighter.

you can build unique new building on the moon.
the jumpgate and Sensor Phalanx

Fleet leaving moon can't be scan by Sensor Phalanx.
so it;s safer to FS from you moon.