Yes, of course. You either need to make sure that the door itself is a separate object and the pivot is in the right place, or you need to rig it as a skeletal mesh.
So in fact, I can export one single model with home and door, but this door will be as a separate piece, and I will be able to manage it? Or Door and house should be separate meshes?
Sorry, found the video is private, now it is open. What if I want to have one house and its door in one FBX file, but Door is not connected to the house mesh, it is a separate piece of mesh but in the group of the house. In unity I can import one fbx with house and door in it, and I can move separate parts of the same model