As CR states, after an appeal both parties have a month to decide whether they want to start the process of possibly appealing further, by requesting a Statement of Reasons from the Tribunal, however this must be done within a month of the Decision, so if your appeal was 12th September and no Statement of Reasons has been requested then they are now out of time and need to pay your award.
To check this, call the Tribunals Service and ask if a Statement of Reasons has been requested, if it hasn't then call the DWP back and complain, advising them they are out of time to consider appeal and must pay your award.
If they do request a Statement of Reasons then it's a waiting game I'm afraid as to whether they will actually appeal. As CR states, they can only do this on an error of law.
Hope this helps.