Just as another solution:
Instead of creating the second column, you can categorize your string data(month name) and sort by that like this:
df.rename(columns={1:'month'},inplace=True)
df['month'] = pd.Categorical(df['month'],categories=['December','November','October','September','August','July','June','May','April','March','February','January'],ordered=True)
df = df.sort_values('month',ascending=False)
It will give you the ordered data by month name as you specified while creating the Categorical object.