Hey there, UnrezolvedKaos.
Root is not supported by all manufacturers, thus this might be illegal. Fortunately this does not require that you have you phone rooted so, just go ahead and download a backup app from the store, or just move the data by using a file manager. Note that you probably won't be able to move apps (maybe some of their data but not the whole app), but you should be able to move your personal files (photos, videos, music, documents, etc).
Hope that helps.
Boogieman_WD