Hi Lamb and welcome to our Forum!
Another thing that's good to know about young Sims moving out is that you can kick them out and it doesn't cost you anything. The Sim who wants to move just uses a phone or computer and selects "Move" from the options. When the moving screen comes up, click the "Kick Out" box. The Sim will take possession of an empty house somewhere in town. You'll need to follow him/her to see where the new place is. Then if you want to play that Sim again, go to Edit Town and change the active household. Beware, though, when you change active households, you will lose all the wishes of your original household. They will also continue with their lives while you are away and you could come back to find lots of changes in the family.