It is possible to copy a Mobile Data Entry Profile within the same Configuration Pack by using the Admin Portal. However, to copy  to another configuration pack, OpenGround Professional is required. This is done via the Manage Components dialog.

1. Select the source configuration pack 
2. Click 'Manage Components' and select 'Mobile Data Entry Profiles' from the Component Type dropdown
3. Select the profiles to export, click Export - and save the resulting HBC file
4. Select the target config pack
5. Click 'Import Components' and navigate to the previously saved HBC file
6. Click Import

Important Notes:

1. If the target config pack already has profiles matching the names of the profiles being imported, these profiles will be completely replaced with the new profiles.
2. A successful profile import relies on the target config pack having a compatible model (e.g. Group names, Headers within a Group, PickList Groups, etc) for anything that is referenced by the profile. If this is not the case, then the import process will import as much as it is able to - but will then display validation errors for anything that it was unable to import.