You don't really need the index, you could just compare two rows and use that to filter the columns with a list comprehension.
df = pd.DataFrame({"col1": np.ones(10), "col2": np.ones(10), "col3": range(2,12)})
row1 = df.irow(0)
row2 = df.irow(1)
unique_columns = row1 != row2
cols = [colname for colname, unique_column in zip(df.columns, bools) if unique_column]
print cols # ['col3']
If you know the standard value for each column, you can convert all the rows to a list of booleans, i.e.:
standard_row = np.ones(3)
columns = df.columns
unique_columns = df.apply(lambda x: x != standard_row, axis=1)
unique_columns.apply(lambda x: [col for col, unique_column in zip(columns, x) if unique_column], axis=1)