Single word to describe a single planet and all its moons?

How about just planet region?

Consider this:

We're now passing through the Jupiter region with its remarkable satellites.

The region would suggest it's a planet and a little extra. Since planet's satellites are orders of magnitude closer to the planet than any other celestial objects, it is safe to assume they belong to the region implicitly.

If the planet has a name, then (the adjectival form of) the planet's name followed by system seems common in both SF and real usage.

For example the Martian system comprises Mars, Phobos and Deimos. The phrase is widely used online.

Earth system doesn't appear to be widely used in this context. Earth-moon system is used in some discussions while the use of Terran system seems to be confined (almost) to SF.

See planetary system at Wikipedia.

A planetary system is a set of gravitationally bound non-stellar objects in orbit around a star or star system.

Go here at space/stackexchange and have a look.