There is a plugin available that will do the job.
- Download "doublesave.zip" from here.  
- Extract the contents and copy doublesave.pluginanddoublesave.pyto~/.local/share/gedit/plugins. If the folder does not exist, you will need to create it.
- Also create ~/gedit-backupsbecause the backup files will be stored here.
 Open gedit and enable the Doublesave plugin: select Edit  ▸ Preferences ▸ Plugins ▸ [Name of Plugin] to enable the plugin.
From now on, each time you save a file in gedit while working, a timestamped backup is created in ~/gedit-backups.
It is also possible to tweak some things. For example, I've recently installed Dropbox and wanted to have gedit-backups in my Dropbox folder rather than in ~/home/user. And I preferred my timestamp to be %Y%m%d%H%M%S rather than %Y_%m_%d-%H_%M_%S.
To make both those changes, edit ~/.local/share/gedit/plugins/doublesave.py.