Is there a way to copy only the structure (not the data) of a Pandas DataFrame?

That’s a job for reindex_like. Start with the original:

df1 = pd.DataFrame([[11, 12], [21, 22]], columns=['c1', 'c2'], index=['i1', 'i2'])

Construct an empty DataFrame and reindex it like df1:

pd.DataFrame().reindex_like(df1)
Out: 
    c1  c2
i1 NaN NaN
i2 NaN NaN