BUG: merge_asof result index type not set
- [x] I have checked that this issue has not already been reported.

- [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.

---

**Note**: Please read [this guide](https://matthewrocklin.com/blog/work/2018/02/28/minimal-bug-reports) detailing how to provide the necessary information for us to reproduce your bug.

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

```python

dates_df = pd.DataFrame(pd.Series(name='col_name', dtype='object'), index=pd.DatetimeIndex([], name='time', freq=None))
dates_df.index = dates_df.index.tz_localize('UTC')

weights_time = pd.date_range(start='20200101', end='20200110')
weights_time = weights_time.tz_localize('UTC')

weights_df = pd.DataFrame(index=weights_time)
weights_df['col_name'] = 'model1'
weights_df['attr'] = 1.5

joined_df = pd.merge_asof(
    dates_df,
    weights_df,
    by="col_name",
    left_index=True,
    right_index=True,
    direction="backward",
)
```
#### Problem description
The two input dataframes (dates_df and weights_df) have a DatetimeIndex, but the resulting joined_df does not. 

#### Expected Output
I would expect the resulting index to be a DatetimeIndex and have type 'datetime64[ns, UTC]'

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

<details>

INSTALLED VERSIONS
------------------
commit           : None
python           : 3.7.9.final.0
python-bits      : 64
OS               : Linux
OS-release       : 4.14.67-ts1
machine          : x86_64
processor        : 
byteorder        : little
LC_ALL           : None
LANG             : en_US.utf8
LOCALE           : en_US.UTF-8

pandas           : 1.0.5
numpy            : 1.16.6
pytz             : 2020.4
dateutil         : 2.8.0
pip              : 19.3.1
setuptools       : 42.0.2
Cython           : 0.29.21
pytest           : 5.3.1
hypothesis       : 6.0.3
sphinx           : 3.4.3
blosc            : 1.5.1
feather          : None
xlsxwriter       : 1.0.2
lxml.etree       : 4.5.2
html5lib         : 1.0.1
pymysql          : None
psycopg2         : 2.8.6 (dt dec pq3 ext lo64)
jinja2           : 2.11.1
IPython          : 7.14.0
pandas_datareader: None
bs4              : 4.9.1
bottleneck       : 1.2.1
fastparquet      : 0.4.1
gcsfs            : 0.6.1
lxml.etree       : 4.5.2
matplotlib       : 3.0.3
numexpr          : 2.6.4
odfpy            : None
openpyxl         : None
pandas_gbq       : None
pyarrow          : 1.0.1
pytables         : None
pytest           : 5.3.1
pyxlsb           : None
s3fs             : 0.4.2
scipy            : 1.5.1
sqlalchemy       : 1.3.18
tables           : 3.6.1
tabulate         : 0.8.3
xarray           : 0.16.2
xlrd             : 1.1.0
xlwt             : 1.3.0
xlsxwriter       : 1.0.2
numba            : 0.53.0

</details>
