BUG: Empty DataFrame(..., dtype='datetime64[ns]').quantile(..., axis=1) returns float64 dtype
- [ ] xref #41544 
- [ ] tests added / passed
- [ ] Ensure all linting tests pass, see [here](https://pandas.pydata.org/pandas-docs/dev/development/contributing.html#code-standards) for how to run them
- [ ] whatsnew entry

@mroeschke

`quantile` passes the test mentioned in #41544 with the code in 9317cfd. 

There may be other problematic cases not covered by the test:

1. Should the dtype of the resulting series ideally be 'object' here (due to mixed dtypes in the DataFrame)?
```
In [1]: df = DataFrame(columns=["a", "b"], dtype="datetime64[ns]")
In [2]: df["b"] = df["b"].view("int64")
In [3]: df.quantile(0.5, axis=1, numeric_only=False).dtype
Out [1]: dtype('float64')
```

2. Should the dtype of the result be datetime64[ns] here?
```
In [1]: df = DataFrame(columns=["a", "b"], dtype="datetime64[ns]")
In [2]: df.quantile([0.1, 0.5], axis=1, numeric_only=False).dtypes
Out [1]: Series([], dtype: object)
```
I can address both 'problems' if so. This pull request is stale because it has been open for thirty days with no activity. Please update or respond to this comment if you're still interested in working on this. Thanks for the PR, but I think since there are some edge cases not entirely figured out yet, I think its best that those issues are first discussed in the original issue first before proceeding here. Happy to have you contribute to that discussion or work on other issues.