You can copy the active version of a document to another folder. When you do so, you have the option to copy or not copy all of its versions as well. When you copy the active version and its versions, the Sequence and Version properties of the copied versions will match the Sequence and Version properties of the source versions. When you copy the active version and choose not to copy its versions along with it, the value of the Sequence property of the copied document will become 0, indicating it is an original document, and the Version property will be blank (which you can edit once copied).
You can also copy a version to another folder, without also copying its active version. Once copied, the version's relationship to the version set in the source folder is broken, and the new copy becomes an original, editable document in the target folder. If you look at the newly created document's properties, the value of the Sequence property is now 0, and the Version property keeps the source version's label.
Just like copying regular documents, to copy a version, your user setting Document - Create must be on, and you must have permission to create documents in the target folder.