That is a pretty good summary. And it is something the church used to talk about a lot. Once they realized it wasn’t a draw, but a scary crazy thing for non-members they go out of their way to all but deny it.
Let me see if I can’t flesh it out though. The basic doctrine goes something like this.
We were all created as spirits before we were incarnated into physical bodies. This was through some divine spiritual conception. According to Mormons we are all brothers and sisters in a far more literal sense than most Christians believe. Christ is our oldest brother and in some other ways is different from the rest of us… but really only in that he was better than any of the rest of us. We are all literally divine and can be co-inheritors of God along with Jesus, if we are only just righteous enough.
When we die, we will eventually end up in one of four places or kingdoms:
The Celestial - This is where God the Father lives. This is reserved for the best of the best. I’ve heard in talks given by church officials that only a few percent of even the church members will make it all the way there. Then again I’ve heard that most of the church members will make it there. And there will be some number of very good people who convert after their deaths who will be here too. Strictly speaking the Earth is supposed to be converted to Celestial matter and move through space to God’s physical location (Kolob). Everyone who makes it there stays on Earth and lives with the Father, Son and Holy Ghost.
The Terrestrial - This is the second rank. Good people who don’t ever accept the church (even after death) and faithless Mormons who still manage to not become too horrible. Christ will live with them (part time) but they never get to see the Father again.
The Telestial - This is the bottom rank. It is still supposed to be so nice that we would all just kill ourselves to get there faster. Out of the Godhead only the Holy Ghost will be in Telestial. This is where really bad people end up (unrepentant murderers, rapists, and the like).
Outer Darkness - This is where the even worst go. This is where Satan and his followers in the original fall will end up. We can get there but only if we “deny the Holy Ghost.” Generally this means only prophets and the like who actively work against God can go there.
So with the basics covered, to your original question. In the Celestial Kingdom there will be separations. The best of these are for couples (neither men nor women can achieve the best unmarried). For them they become “Exalted” and get to live “the kind of life God lives.” They become gods and goddesses. They get to create spirit children, and help their children through the same path of existence that we all are supposed to follow. Getting your own planet isn’t spelled out specifically. And in fact most Mormons believe they’ll get their own universe, not just a planet. After all if we can become like God the Father, we’ll get universes just like he has, right?
The interesting thing is while the outlines of the doctrine are well defined, and spelled out in LDS scriptures, details are sketchy. Exactly how being a god or goddess, and what faithful Mormons are going to get, and how that will work is left to the individual members. So in the 19th century you get a lot of references to getting a planet. That is what the members could imagine. Evidently members have bigger imaginations now in the 21st century. 