Maybe "planetary system" is a system of planets, but a "planet system", like the "Jupiter system", would be the system for a single planet. That would make "stellar system" sensible too. Furthermore, a planetary system associated with a single star is a "star system".

One more option: "exosolar system".

Nitpicks:

First, I would call it the Solar System. (Not any solar system, mind you.) That would be in line with existing nomenclature in which the Solar System¹ is the name of our planetary system².

Second, "moon" is not the best term (although I know it's in use like a lot of other "liberal English" words) and I would prefer "(natural) satellite"³ for this generic meaning and leave "moon" for the (Earth's) Moon⁴.

¹ https://en.wikipedia.org/wiki/Solar_System

² https://en.wikipedia.org/wiki/Planetary_system

³ https://en.wikipedia.org/wiki/Natural_satellite

⁴ https://en.wikipedia.org/wiki/Moon