BUG: DataFrame.reset_index() discards MultiIndex dtypes if DataFrame is empty

[batterseapower]

• I have checked that this issue has not already been reported.
• I have confirmed this bug exists on the latest version of pandas. (tried on v1.0.5 -- the latest in Conda -- and checked the release notes for the new version to make sure they don't mention anything related)
• (optional) I have confirmed this bug exists on the master branch of pandas.

---

Code Sample, a copy-pastable example

x = pd.DataFrame.from_dict({
    'A': pd.Categorical.from_codes([1], categories=['G', 'H']),
    'B': np.array([0], dtype='i8'),
})

x.dtypes # category and int64

# This is the bug:
x.iloc[:0].set_index(['A', 'B']).reset_index().dtypes # float64 and float64

# These cases all work correctly i.e. the dtypes are category and int64
x.set_index(['A', 'B']).reset_index().dtypes
x.set_index('A').reset_index().dtypes
x.iloc[:0].set_index('A').reset_index().dtypes

# This is CategoricalDtype as expected, so the MultiIndex construction is correct: it's just the `reset_index()` which is throwing away the info
x.iloc[:0].set_index(['A', 'B']).index.get_level_values('A').dtype

Problem description

reset_index shouldn't throw away dtype information in the special case where the DataFrame has zero rows. Sometimes it's hard to avoid throwing away info when you manipulate zero-element DataFrames, but in this case there is no reason to do it.

Expected Output

category and int64 dtypes from reset_index in all cases

Output of pd.show_versions()

INSTALLED VERSIONS

commit : None
python : 3.8.5.final.0
python-bits : 64
OS : Windows
OS-release : 10
machine : AMD64
processor : Intel64 Family 6 Model 63 Stepping 2, GenuineIntel
byteorder : little
LC_ALL : None
LANG : None
LOCALE : English_United Kingdom.936

pandas : 1.0.5
numpy : 1.19.1
pytz : 2020.1
dateutil : 2.8.1
pip : 20.1.1
setuptools : 49.2.0.post20200714
Cython : None
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : None
IPython : 7.16.1
pandas_datareader: None
bs4 : None
bottleneck : 1.3.2
fastparquet : None
gcsfs : None
lxml.etree : None
matplotlib : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : None
pytables : None
pytest : None
pyxlsb : None
s3fs : None
scipy : 1.5.0
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
xlwt : None
xlsxwriter : None
numba : None

[TomAugspurger]

This sounds like #19602. Can you try with pandas 1.1?

[TomAugspurger]

Just tried with master, and I see

# This is the bug:
x.iloc[:0].set_index(['A', 'B']).reset_index().dtypes # float64 and float64

## -- End pasted text --
Out[3]:
A    category
B       int64
dtype: object

so I think we're good. LMK if not and we'll reopen.