BUG: set_index screws up the dtypes on empty DataFrames
- [x] I have checked that this issue has not already been reported.

  #30517 is similar in concept but relates to non-empty DataFrames, whereas the current bug is about empty ones.

- [x] I have confirmed this bug exists on the latest version of pandas.

- [ ] (optional) I have confirmed this bug exists on the master branch of pandas.

---

#### Code Sample, a copy-pastable example

```python
import pandas
d1 = pandas.DataFrame({'a': pandas.Series(dtype='datetime64[ns]'), 'b': pandas.Series(dtype='int64'), 'c': []})
d2 = d1.set_index(['a', 'b'])
assert (d1.loc[:, ['a', 'b']].dtypes == d2.index.to_frame().dtypes).all()
```

```
>>> d1.loc[:, ['a', 'b']].dtypes
a    datetime64[ns]
b             int64
dtype: object
>> d2.index.to_frame().dtypes
a    object
b     int64
dtype: object
```

#### Problem description

The dtype of the columns are silently changed when `.set_index` is called. This only happens when the DataFrame is empty, which suggests that this is an edge-case bug.

This is problematic because the behavior of `.set_index()` varies depending on whether the DataFrame has any rows.

#### Expected Output

The assertions should not fail.

#### Output of ``pd.show_versions()``

<details>

```
INSTALLED VERSIONS
------------------
commit           : b5958ee1999e9aead1938c0bba2b674378807b3d
python           : 3.9.0.final.0
python-bits      : 64
OS               : Linux
OS-release       : 5.9.13-arch1-1
Version          : #1 SMP PREEMPT Tue, 08 Dec 2020 12:09:55 +0000
machine          : x86_64
processor        : 
byteorder        : little
LC_ALL           : None
LANG             : en_FYL.UTF-8
LOCALE           : en_US.UTF-8

pandas           : 1.1.5
numpy            : 1.19.4
pytz             : 2020.4
dateutil         : 2.8.1
pip              : 20.2.1
setuptools       : 50.3.2
Cython           : None
pytest           : None
hypothesis       : None
sphinx           : None
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : 4.6.2
html5lib         : 1.1
pymysql          : None
psycopg2         : None
jinja2           : 2.11.2
IPython          : 7.19.0
pandas_datareader: None
bs4              : 4.9.3
bottleneck       : None
fsspec           : None
fastparquet      : None
gcsfs            : None
matplotlib       : 3.3.3
numexpr          : None
odfpy            : None
openpyxl         : None
pandas_gbq       : None
pyarrow          : None
pytables         : None
pyxlsb           : None
s3fs             : None
scipy            : 1.5.4
sqlalchemy       : 1.3.20
tables           : None
tabulate         : None
xarray           : None
xlrd             : None
xlwt             : None
numba            : None
```

</details>
